G-matrix Fourier transformation (GFT) nuclear magnetic resonance (NMR) experiments for resonance assignment and structure determination of organic molecules

ABSTRACT

The present invention discloses a suite of G 2 FT and GFT NMR experiments that can be used for complete resonance assignments of proteins and for obtaining structural (conformational and orientational) constraints for determining high resolution three-dimensional structures of biomolecules.

This application claims the benefit of U.S. Provisional PatentApplication Ser. No. 60/620,070, filed Oct. 18, 2004, and U.S.Provisional Patent Application Ser. No. 60/701,429, filed Jul. 21, 2005,which are hereby incorporated by reference in their entirety.

This invention arose out of research sponsored by the NationalInstitutes of Health (Grant No. P50 GM62413-01) and the National ScienceFoundation (Grant Nos. MCB 00075773 and 0416899). The U.S. Governmentmay have certain rights in this invention.

FIELD OF THE INVENTION

The present invention relates to methods of conducting G-matrix Fouriertransformation (GFT) nuclear magnetic resonance (NMR) experiments forresonance assignment and structure determination of organic molecules.

BACKGROUND OF THE INVENTION

Multidimensional nuclear magnetic resonance (NMR) spectroscopy ispivotal for pursuing NMR-based structural biology (Cavanagh et al.,Protein NMR Spectroscopy Academic Press: San Diego (1996); Wüthrich, NMRof proteins and Nucleic Acids Wiley: New York (1986)). In manyinstances, it is desirable to obtain multidimensional spectralinformation as rapidly as possible. First, the costs related tospectrometer usage are reduced and the throughput of samples per NMRspectrometer can be increased. Second, the requirement for longevity ofNMR samples is alleviated. Third, a higher time resolution can beachieved to study dynamic processes by multidimensional spectra. Thefirst two objectives are at the heart of NMR-based structural genomics,which aims at establishing NMR spectroscopy as a powerful tool forexploring protein “fold space” and yielding at least one experimentalstructure for each family of protein sequence homologues (Montelione etal., Nat. Struc. Biol. 7:982-984 (2000)).

Fast acquisition of multidimensional spectra, however, is limited by theneed to sample (several) indirect dimensions. This restriction can becoined the “NMR sampling problem”; above a threshold at which themeasurement time is long enough to ensure a workable signal-to-noiseratio (S/N), the sampling of indirect dimensions determines therequirement for instrument time. In this “sampling-limited” datacollection regime (Szyperski et al., Proc. Natl. Acad. Sci. USA99:8009-8014 (2002)), valuable instrument time is invested to meet thesampling demand rather than to achieve sufficient “signal averaging.”Hence, techniques to speed up NMR data collection focus on avoiding thisregime, that is, they are devised to push data collection into the“sensitivity-limited” regime in order to properly adjust NMR measurementtime to sensitivity requirements. In view of the well-known fact thatNMR measurement times tend to increase with molecular weight, rapidsampling approaches for accurate adjustment of measurement times on theone hand and methodology developed to study large systems on the other(e.g., transverse relaxation optimized spectroscopy (TROSY; Pervushin etal., Proc. Natl. Acad. Sci. USA 94:12366-12371 (1997)) or proteindeuteration (Gardner et al., Ann. Rev. Biophys. Biomol. Struct.27:357-406 (1998)) are complementary.

The implementation of rapid data collection protocols avoiding samplinglimitations requires that the number of acquired free induction decays(FIDs), i.e., the number of data points sampled in the indirectdimensions, is reduced. Notably, phase-sensitive acquisition of an NDFourier transformation (FT) NMR experiment requires sampling of N−1indirect dimensions with n₁×n₂× . . . ×n_(N-1) complex points,representing 2^(N-1)×(n₁×n₂× . . . ×n_(N-1)) FIDs. There is a steepincrease of the minimal measurement time, T_(m), with dimensionality;acquiring 16 complex points in each indirect dimension (with one scanper FID each second) yields T_(m)(3D)=0.5 hours, T_(m)(4D)=9.1 hours,T_(m)(5D)=12 days, and T_(m)(6D)=1.1 years.

When reducing the number of acquired FIDs, the key challenge is topreserve the multidimensional spectral information that can be obtainedby conventional linear sampling with appropriately long maximalevolution times in all indirect dimensions. Moreover, trimming thenumber of sampled data points may in turn require processing techniquesthat complement, or replace, widely used Fourier transformation of timedomain data.

G-Matrix Fourier Transformation (GFT) NMR Spectroscopy

G-matrix Fourier Transformation (GFT) NMR spectroscopy (Kim et al., J.Am. Chem. Soc. 125:1385-1393 (2003)) represents a generalization ofreduced dimensionality (RD) NMR spectroscopy and aims at providinghigh-dimensional spectral information with both accuracy and speed. GFTNMR spectroscopy results from “modules” derived for RD NMR and combinesmultiple phase-sensitive RD NMR, multiple “bottom-up” central peakdetection, and (time domain) editing of the components of the chemicalshift multiplets. This resulting data acquisition scheme requiresadditional processing of time domain data, the so called “G-matrix”transformation. Hence, the acronym “GFT” indicates a combined G-matrixand Fourier transformation.

The phase-sensitive joint sampling of several indirect dimensions of ahigh-dimensional NMR experiment requires that the spectral width,SW_(GFT), in the resulting combined “GFT-dimension” is set toSW_(GFT)=Σκ_(j) SW_(j), where SW_(j) and κ_(j) represent, respectively,the jth spectral width and the factor to scale the sampling incrementsof the jth dimension, which enable adjustment for maximal evolutiontimes (Kim et al., J. Am. Chem. Soc. 125:1385-1393 (2003)). As a result,the “sampling demand” increases only linearly when dimensions are addedfor joint sampling, that is, the minimal measurement time of a GFT NMRexperiment scales with the sum of the number of complex points requiredto sample the individual dimensions. In sharp contrast, the minimalmeasurement time of a conventional multidimensional NMR scales with theproduct of the number of complex points. Hence, employment of GFT NMRmakes it possible to reduce measurement times by about an order ofmagnitude for each dimension that is being added to the joint samplingscheme.

As described in Szyperski et al., J. Biomol. NMR 3:127-132 (1993),Szyperski et al., J. Am. Chem. Soc. 115:9307 (1993), Szyperski et al.,J. Magn. Reson. B105:188-191 (1994), and Szyperski et al., J. Magn.Reson. B108:197-203 (1995), RD NMR yields doublets (“peak pairs”) thatarise from the joint sampling of two chemical shift evolution periods.In GFT NMR, the joint sampling of several shift evolution periodsgenerates more complicated multiplet structures, which were named“chemical shift multiplets” (Kim et al., J. Am. Chem. Soc. 125:1385-1393(2003)). If all projected shifts are measured in a cosine-modulatedfashion, the components of the chemical shift multiplet are all inphase.Depending on which and how many shifts are measured in a sine-modulatedmanner, various components become antiphase. Recording of allcombinations of cosine and sine modulations then allows the componentsof the shift multiplet to be edited into subspectra. In particular,G-matrix transformation enables this editing to be performed in the timedomain. This is advantageous when linear prediction of time domain datais applied, because the S/N for each multiplet component is increasedwhile a single component remains after editing for each subspectrum.

The GFT NMR formalism embodies a generally applicable NMR dataacquisition scheme (Kim et al., J. Am. Chem. Soc. 125:1385-1393 (2003)).If m=K+1 chemical shift evolution periods of an ND experiment arejointly sampled in a single indirect GFT dimension, 2^(m)−1 different(N−K)D spectra represent the GFT NMR experiment containing theinformation of the parent ND experiment. Hence, such a set of 2^(m)−1subspectra is named an (N,N−K)D GFT NMR experiment. For example, a(5,2)D HACACONHN GFT NMR experiment can be recorded for a 8.6 kDaprotein with four scans per real increment in 138 minutes, i.e., theminimal measurement time with a single scan per increment amounts to 33minutes. In contrast, a conventional 5D HACACONHN NMR sampled with10(t₁/¹H^(α))×11(t₂/¹³C^(α))×22(t₃/¹³C′)×13(t₄/¹⁵N)×512(t₅/¹HN) complexdata points would have required 5.8 days of spectrometer time with asingle scan per real data point. Thus, a 250-fold reduction in minimalmeasurement time could be achieved with GFT NMR. Moreover, the processed(5,2)D HACACONHN frequency domain data have a total size of 16 MByte,while a hypothetical 5D spectrum with the same digital resolution wouldrepresent a file of 618 GByte. Hence, employment of GFT NMR allowsaccurate adaptation of measurement times without sacrificing digitalresolution.

Chemical shifts are multiply encoded in the shift multiplets registeredin GFT NMR experiments. This corresponds to performing statisticallyindependent multiple measurements, so that the chemical shifts can beobtained with high precision (Kim et al., J. Am. Chem. Soc.125:1385-1393 (2003); Kim et al., J. Biomol. NMR 28:117-130 (2004)).Moreover, the well-defined peak pattern of the shift multiplets allowsimplementation of robust algorithms for peak picking (Moseley et al., J.Magn. Reson. 170:263-277 (2004)). Both features make GFT NMR highlyamenable to automated analysis. Although GFT NMR has been shown to aidin high-throughput protein resonance assignments by enabling both fastand precise acquisition of high dimensional spectral information,spectral overlap can still hamper resonance assignments in largeproteins.

NMR of Aromatic Rings in Protein

Aromatic amino acids in proteins have long attracted the attention ofstructural biologists due to their important role for the hydrophobiccore. From structural studies using NMR spectroscopy, it is known that(i) aromatic rings in the molecular core provide a large number ofcrucial ¹H—¹H nuclear Overhauser effects (NOEs) required for obtaining ahigh-quality structure (Wüthrich, NMR of Proteins and Nucleic AcidsWiley: New York (1986); Smith et al., J. Biomol. NMR 8:360-368 (1996);Aghazadeh et al., Nature Struct. Biol. 5:1098-1107 (1998); Clore et al.,J. Am. Chem. Soc. 121:6513-6514 (1999); Medek et al., J. Biomol. NMR18:229-238 (2000); Shen et al., J. Am. Chem. Soc. 127:9085-9099 (2005))and that (ii) aromatic rings flip about the χ²-angle (Wagner, Quat. Rev.Biophys. 16:1-57 (1983)). The flipping of the rings in the close-packedinterior of a protein requires large movements of the surrounding atomsand, thus, provides invaluable information on larger-amplitude motionalmodes and protein dynamics (Skalicky et al., J. Am. Chem. Soc.123:388-397 (2001)). Hence, sequence specific NMR assignment of aromaticresonances in proteins is of central importance for NMR-based structuralstudies.

Prior to the advent of multidimensional NMR spectroscopy, assignments ofaromatic rings relied on combined use of one-dimensional (1D) spindecoupling experiments (Wagner et al., J. Magn. Reson. 20:565-569(1975)), selective chemical modification (Snyder et al., Biochemistry14:3765-3777 (1975)), or comparison of spectra of homologous proteins(Wagner et al., Eur. J. Biochem. 89:367-377 (1978)). Subsequently, theintroduction of 2D [¹H,¹H]-NOESY and COSY facilitated resonanceassignments in unlabeled proteins. An important addition was 2D [¹³C,¹H]COSY and 2D [¹³C,¹H] relayed COSY (Brühwiler et al., J. Magn. Reson.69:546-551 (1986); Wagner et al., Biochemistry 25:5839-5843 (1986)),which provided higher resolution for the ¹H lines of aromatic rings(Wagner et al., J. Mol. Biol. 196 :227-231 (1987)) and which weretypically acquired at natural ¹³C abundance. However, these techniqueswere limited to small proteins (molecular weight <10 kDa). For proteinscontaining a large numbers of aromatic residues, spectral overlap in 2Drenders complete assignment of the aromatic resonances difficult orimpossible.

With the advent of ¹³C/¹⁵N isotope labeling of proteins, numerousadditional multidimensional NMR experiments for the assignment ofaromatic rings have been proposed (Kay et al., J. Magn. Reson.B101:333-337 (1993); Yamazaki et al., J. Am. Chem. Soc. 115:11054-11055(1993); Grzesiek et al., J. Am. Chem. Soc. 117:6527-6531 (1995); Zerbeet al., J. Biomol. NMR 7:99-106 (1996); Carlomagno et al., J. Biomol.NMR 8:161-170 (1996); Löhr et al., J. Magn. Reson. B112:259-268 (1996);Whitehead et al., J. Biomol. NMR 9:313-316 (1997); Prompers et al., J.Magn. Reson. 130:68-75 (1998); Löhr et al., J. Biomol. NMR 22:153-164(2002)). The most commonly used approach is to first obtain spin systemassignments within the aromatic rings using one-bond scalar couplings,followed by use of 3D/4D heteronuclear resolved [¹H,¹H]-NOESY forlinking the aromatic resonances to those of the aliphatic side-chainmoieties (Cavanagh et al., Protein NMR Spectroscopy: Principles andPractice Academic Press: San Diego (1996)). Alternatively, scalarcouplings can be used to connect aliphatic and aromatic spins via¹³C^(γ) spins (Yamazaki et al., J. Am. Chem. Soc. 115:11054-11055(1993); Löhr et al., J. Magn. Reson. B112:259-268 (1996); Prompers etal., J. Magn. Reson. 130:68-75 (1998)). In parallel, novel isotopelabeling strategies have been developed for aromatic rings whichalleviate the loss of sensitivity due to broad ¹H lines and passive¹³C-¹³C couplings. These include the reverse labeling scheme (Vuister etal., J. Am. Chem. Soc. 116:9206-9210 (1994)), atom-type specificlabeling (Wang et al., J. Am. Chem. Soc. 121:1611-1612 (1999)),biosynthetically directed fractional ¹³C-labeling (Szyperski et al., J.Biomol. NMR 2:323-334 (1992); Jacob et al., J. Biomol. NMR 24:231-235(2002)), and selective protonation of aromatic rings in an otherwisefully deuterated protein (Rajesh et al., J. Biomol. NMR 27:81-86(2003)).

For large proteins, HCCH spectroscopy, first introduced for aliphaticside-chain assignments (Kay et al., J. Am. Chem. Soc. 112:888-889(1990)), has emerged as an efficient means to accomplish aromatic spinsystem identification. Experiments in this class include 3D (H)CCH and3D H(C)CH (Cavanagh et al., Protein NMR Spectroscopy: Principles andPractice Academic Press: San Diego (1996)). Their combination with TROSY(Pervushin et al., Proc. Natl. Acad. Sci. USA 94:12366-12371 (1997)) hasbeen shown to yield higher sensitivity (Pervushin et al., J. Am. Chem.Soc. 120:6394-6400 (1998); Meissner et al., J. Magn. Reson. 139:447-450(1999)), thereby extending the molecular weight limit of proteinsaccessible to these experiments (i.e., for proteins in the“sensitivity-limited” regime (Szyperski et al., Proc. Natl. Acad. Sci.USA 99:8009-8014 (2002)). However, HCCH-type experiments suffer from thecomparably low dispersion of aromatic ¹³C/¹H shifts, making itadvantageous to use 4D HCCH (note that good spectral resolution is alsoimportant for exploring aromatic ring flipping since accurateline-widths need to be measured (Skalicky et al., J. Am. Chem. Soc.123:388-397 (2001)). The 4D experiments would, however, lead toincreased minimal measurement times which may lead to sampling-limiteddata acquisition (Szyperski et al., Proc. Natl. Acad. Sci. USA99:8009-8014 (2002)). Thus, an implementation that provides 4Dinformation while being suited for both sensitivity and sampling limiteddata collection has not been available.

Nuclear Overhauser Effect Spectroscopy (NOESY)

Efficient NMR-based protein structure determination (Wüthrich, NMR ofProteins and Nucleic Acids Wiley: New York (1986)) relies on measurementof nuclear Overhauser effects (NOEs), which yield ¹H-¹H upper distancelimit constraints. The assignment of NOEs quite generally depends onhaving (nearly) complete resonance assignments (Wüthrich, NMR ofProteins and Nucleic Acids Wiley: New York (1986); Cavanagh et al.,Protein NMR Spectroscopy Academic Press: San Diego (1996)). However, dueto the degeneracy of chemical shifts, the NOE assignment remains anon-trivial task even when complete resonance assignments are available.Nowadays, two approaches are routinely used to solve this “NOEassignment problem”. First, proteins are ¹⁵N/¹³C double labeled(Kainosho, Nature Struc. Biol. 4:858-861 (1997); Acton, Methods Enzymol.394:210-243 (2005)) so that NOEs can be measured in 3D ¹⁵N- or¹³C-resolved [¹H,¹H]-NOE spectroscopy (NOESY) (Cavanagh et al., ProteinNMR Spectroscopy Academic Press: San Diego (1996)). Dispersing NOEsignals in a third dimension, which encodes a ¹³C or a ¹⁵N shift,typically allows one to assign for medium-sized proteins ˜15-25% of theNOEs directly based on chemical shift data (compared to only a fewpercent in 2D [¹H,¹H]-NOESY (Wüthrich, NMR of Proteins and Nucleic AcidsWiley: New York (1986); Cavanagh et al., Protein NMR Spectroscopy,Academic Press: San Diego (1996)). Second, an initial structure iscalculated which is used in conjunction with the chemical shifts toassign additional NOEs. Several such cycles of structure calculation andNOE assignment are usually performed iteratively until a refinedstructure is obtained.

Importantly, inaccuracies in the initial fold arising from incorrectlyassigned NOEs may result in the mis-assignment of additional NOEs.Hence, proper convergence of the NMR structure determination depends onobtaining an appropriately accurate initial structure, i.e., it isadvantageous if the bundle of conformers representing the initialsolution structure covers a conformational subspace which overlaps withthat of the refined ensemble of conformers. This requirement constitutesa key challenge for reliable automated NOE assignment (Güntert, Prog.NMR Spectroscopy 43:105-125 (2003); Baran et al., Chem. Reviews104:3451-3455 (2004); Huang et al., Methods Enzymol. 394:111-141 (2005))and, thus, also for the development of a robust and scalable platformfor high-throughput structure determination in structural genomics(Montelione et al., Nature Struc. Biol. 7:982-984 (2000); Yee et al.,Proc. Natl. Acad. Sci. USA 99:1825-1830 (2002)). Several programs havebeen established to automatically obtain accurate initial folds(Güntert, Prog. NMR Spectroscopy 43:105-125 (2003); Baran et al., Chem.Reviews 104:3451-3455 (2004); Huang et al., Methods Enzymol. 394:111-141(2005)). Among those are AutoStructure (Moseley et al., Methods Enzymol.339:91-108 (2001); Huang et al., J. Mol. Biol. 327:521-536 (2003); Huanget al., J. Am. Chem. Soc. 127:1665-1674 (2005)) and CYANA (Güntert etal., J. Mol. Biol. 273:283-298 (1997); Herrmann et al., J. Mol. Biol.319:209-227 (2002); Güntert, Methods Mol. Biol. 278:347-372 (2004)),both of which are widely used. Conceptually, AutoStructure mimics theapproach an expert usually takes when solving a structure manually. Theinitial fold is generated based on (i) intraresidue, sequential, andmedium-range NOEs considering NOE patterns of secondary structure, and(ii) unique long-range packing constraints. In contrast, CYANA relies onNOE network-anchoring and combination of (ambiguous) upper distancelimit constraints. This led Montelione et al. to classify theAutoStructure and CYANA approaches as being “bottom-up” and “top-down”,respectively (Baran et al., Chem. Reviews 104:3451-3455 (2004)). Sincethe two programs use distinctly different algorithms, their coupledoperation aiming at a consensus NOE assignment promises to furtherincrease the reliability of initial structure calculations.

In the early 1990s, before the more sophisticated computationaltechniques (Güntert, Prog. NMR Spectroscopy 43:105-125 (2003); Baran etal., Chem. Reviews 104:3451-3455 (2004); Huang et al., Methods Enzymol.394:111-141 (2005)) mentioned above were established, researchersdevised 4D heteronuclear resolved [¹H,¹H]-NOESY and explored its impactfor NMR structure determination of proteins (Kay et al., Science249:411-414 (1990); Clore et al., Biochemistry 30:12-18 (1991);Fairbrother et al., Biochemistry 31:4413-4425 (1992); Grzesiek et al.,Biochemistry 31:8180-8190 (1992); Archer et al., Biochemistry32:6680-6687 (1993); Vuister et al., J. Magn. Reson. B101:210-213(1993)). Such 4D NOESY represents a straightforward and robust approachto tackle the “initial fold problem”; dispersing signals in a fourthdimension enables one to assign the majority of NOEs directly based onchemical shift data. This may yield a highly accurate initial structureso that fast and reliable convergence of the structure determination canbe accomplished. However, 4D NOESY suffers from two major drawbacks,which gave a competitive edge to computational methods in recent years.First, an additional heteronuclear polarization transfer needs to beinserted in the radiofrequency (r.f.) pulse scheme. This leads toadditional losses arising from transverse relaxation and tends to limitthe use of 4D NOESY to small and medium-sized proteins. Second,conventional sampling of three indirect dimensions leads to long(minimal) measurement times. Typically, several days to a week arerequired to collect a single data set, even when accepting comparablyshort maximal evolution times (which limits the spectral resolution).This drawback is further exacerbated if a (minimal) radiofrequency(r.f.) phase cycle is employed for artefact suppression (Cavanagh etal., Protein NMR Spectroscopy Academic Press: San Diego (1996)).

The first drawback of 4D NOESY, i.e., its low sensitivity, has beensignificantly alleviated by the commercial introduction of cryogenic NMRprobes (Styles et al., Magn. Reson. 60:397-404 (1994)), which routinelydeliver about three-fold higher sensitivity compared to conventionalprobes (Monleon et al., J. Struc. Func. Genomics 2:93-101 (2002)). Amongthe various options (Atreya et al., Methods Enzymol. 394:78-108 (2005))to reduce the long minimal measurement times of heteronuclear NOESY,simultaneous (“time-shared”) acquisition of ¹⁵N- and ¹³C-resolved NOESY(Farmer et al., J. Biomol. NMR 4:673-687 (1994); Pascal et al., J. Magn.Reson. 103:197-201 (1994); Jerala et al., J. Magn. Reson. B108:294-298(1995); Uhrin et al., J. Biomol. NMR 18:253-259 (2000); Xia et al., J.Biomol. NMR 27:193-203 (2003)), extensive signal aliasing (Morshauser etal., J. Magn. Reson. 139:232-239 (1999)), and the employment of the RDapproach (Szyperski et al., J. Am. Chem. Soc. 115:9307-9308 (1993);Szyperski et al., J. Magn. Reson. B105:188-191 (1994); Brutscher et al.,J. Magn. Reson. B105:77-82 (1994); Szyperski et al., J. Magn. Reson.B108:197-203 (1995); Szyperski et al., J. Am. Chem. Soc. 118:8146-8147(1996); Szyperski et al., J. Biomol. NMR 11:387-405 (1998); Szyperski etal., Proc. Natl. Acad. Sci. USA 99:8009-8014 (2002)) have been proposed(Brutscher et al., J. Magn. Reson. B109:397404 (1995); Kupce et al., J.Magn. Reson. 172:330-333 (2004)). (Notably, rapid sampling techniquesbased on shortening of the relaxation delay between scans, such aslongitudinal relaxation optimization (Pervushin et al., J. Am. Chem.Soc. 124:12898-12902 (2002); Atreya et al., Proc. Natl. Acad. Sci. USA101:9642-9647 (2004)), are not well-suited for NOESY; it is desirable tokeep ¹H steady state magnetization close to its thermal equilibriumvalue in order to avoid an extensive modulation of NOE by T₁(¹H)relaxation.)

Residual Dipolar Couplings

Residual dipolar couplings (RDC) are valuable NMR parameters yielding“orientational” constraints (Prestegard, Nat. Struct. Biol. 5:517-522(1998)) to study biological macromolecules in solution; RDCs are usedfor (i) refining and validating NMR solution structures of single domainproteins (Tolman et al., Proc. Natl. Acad. Sci. USA 92:9279-9283 (1995);Tjandra et al., Science 278:1111-1114 (1997); Tolman, Curr. Opin. Struc.Biol. 11:532-539 (2001); Bax, Protein Sci. 12:1-16 (2003); Lipsitz etal., Ann. Rev. Biophys. Biomol. Struct. 33:387-413 (2004); Prestegard etal., Chem. Rev. 104:3519-3540 (2004)), (ii) determining the relativeorientation of domains in multi-domain proteins and proteins inmacromolecular complexes (Dosset et al., J. Biomol. NMR 20:223-231(2001); Jain et al., J. Mol. Biol. 343:1379-1389 (2004)), (iii)determining the tertiary fold of a protein when only sparse nuclearOverhauser enhancement (NOE) derived distance constraint networks(Wüthrich, NMR of Proteins and Nucleic Acids Wiley: New York, N.Y.(1986)) can be obtained (Delaglio et al., J. Am. Chem. Soc.122:2142-2143 (2000); Fowler et al., J. Mol. Biol. 304:447-460 (2000);Mueller et al. J. Mol. Biol. 300:197-212 (2000); Andrec et al., J.Biomol. NMR 21:335-347 (2001); Hus et al., J. Am. Chem. Soc.123:1541-1542 (2001); Rohl et al., J. Am. Chem. Soc. 124:2723-2729(2002); Giesen et al., J. Biomol. NMR 25:63-71 (2003)), (iv) supportingthe resonance assignment of proteins (Tian et al., J. Am. Chem. Soc.123:11791-11796 (2001); Zweckstetter et al., J. Am. Chem. Soc.123:9490-9491 (2001); Jung et al., J. Biomol. NMR 30:25-35 (2004)), and(v) elucidating protein dynamics (Tolman et al., Nat. Struct. Biol.4:292-297 (1997); Tolman et al., J. Am. Chem. Soc. 123:1416-1424 (2001);Meiler et al., J. Am. Chem. Soc. 125:8072-8073 (2003)). SinceRDC-derived structural constraints can be obtained rapidly, they arealso attractive for structural genomics (Montelione et al., Nat. Struc.Biol. 7:982-984 (2000)). A dense set of orientational constraints can beobtained if different types of RDCs are considered [for example,¹³C^(α)-¹H^(α) (¹D_(CH)), ¹⁵N-¹H^(N) (¹D_(NH)), or ¹⁵N-¹³C′ (¹D_(NC′))couplings]. The tightness of the constraints used for structurecalculations depends on (i) the absence of systematic errors that mayarise from varying conditions present during NMR data acquisition forthe different types of couplings, (ii) the proper identification andassessment of internal motional modes which partially average RDCs(Tolman et al., J. Am. Chem. Soc. 123:1416-1424 (2001); Peti et al., J.Am. Chem. Soc. 124:5822-5833 (2002), and (iii) evidently the precisionof the RDC measurement per se (Tolman et al., Proc. Natl. Acad. Sci. USA92:9279-9283 (1995); Tjandra et al., Science 278:1111-1114 (1997);Tolman et al., J. Am. Chem. Soc. 123:1416-1424 (2001); Bax, Protein Sci.12:1-16 (2003); Lipsitz et al., Ann. Rev. Biophys. Biomol. Struct.33:387-413 (2004); Prestegard et al., Chem. Rev. 104:3519-3540 (2004)).

To minimize systematic errors, it is desirable to measure multiple RDCssimultaneously in a single experiment (Wang et al., J. Am. Chem. Soc.120:7385-7386 (1998); de Alba et al., J. Biomol. NMR 19:63-67 (2001);Bersch et al., J. Biomol. NMR 27:57-67 (2003); Ding et al., J. Am. Chem.Soc. 125:11504-11505 (2003); Permi, J. Biomol. NMR 27:341-349 (2003);Wienk et al., J. Biomol. NMR 25:133-145 (2003); Hoshino et al., J. Magn.Reson. 171:270-276 (2004); Vijayan et al., J. Magn. Reson. 174:245-253(2005)); this ensures that all couplings are obtained with the samespectrometer set-up and radiofrequency (r.f.) pulse duty cycle. Inaddition, it would be advantageous to mutually correlate all RDCs andchemical shifts belonging to a given covalent moiety, thereby breakingchemical shift degeneracy. Frequency labeling in a second indirectdimension to disperse signals is then not required, and large sets ofunambiguously grouped RDCs can be obtained from two-dimensional (2D)plans exhibiting very high resolution in the indirect dimension.Notably, the shorter minimal measurement times of 2D versus 3D NMRapproaches are advantageous when data need to be collected for slowlyprecipitating aligned protein samples; the different types of couplings,if measured separately, may turn out to be inconsistent with a singlealignment tensor (Tolman et al., Proc. Natl. Acad. Sci. USA 92:9279-9283(1995); Tjandra et al., Science 278:1111-1114 (1997); Tolman, Curr.Opin. Struc. Biol. 11:532-539 (2001); Bax, Protein Sci. 12:1-16 (2003);Lipsitz et al., Ann. Rev. Biophys. Biomol. Struct. 33:387-413 (2004);Prestegard et al., Chem. Rev. 104:3519-3540 (2004)).

Simultaneous measurement of RDCs has been implemented using spin stateseparation/selection (IPAP (Ottiger et al., J. Magn. Reson. 131:373-378(1998)), S³E/S³CT (Meissner et al., J. Magn. Reson. 128:92-97 (1997);Sørensen et al., J. Biomol. NMR 10:181-186 (1997)), α/β selection(Andersson et al., J. Biomol. NMR 12:435-441 (1998)) in the indirectdimension in conjunction with E.COSY-type (Andersson et al., J. Biomol.NMR 12:435-441 (1998); Montelione et al., J. Am. Chem. Soc.111:5474-5475 (1989)) techniques, while TROSY (Pervushin et al., Proc.Natl. Acad. Sci. USA 94:12366-12371 (1997)) can be used to increase theprecision of the measurements (Permi, J. Biomol. NMR 27:341-349 (2003);Wienk et al., J. Biomol. NMR 25:133-145 (2003); Hoshino et al., J. Magn.Reson. 171:270-276 (2004)). These experiments suffer, however, fromseveral drawbacks, which are exacerbated if multiple RDCs shall bemeasured simultaneously: (i) The creation of anti-phase magnetizationfor spin state separation requires an additional delay (Andersson etal., J. Biomol. NMR 12:435-441 (1998); Ottiger et al., J. Magn. Reson.131:373-378 (1998)) and results in reduced sensitivity due to transverserelaxation; (ii) In-phase and anti-phase magnetization components relaxdifferentially so that spectral artifacts arise from spin stateselection/separation (Ottiger et al., J. Magn. Reson. 131:373-378(1998)); (iii) When multiple RDCs evolve simultaneously in anon-constant time (Cavanagh et al., Protein NMR Spectroscopy AcademicPress: San Diego, Calif. (1996)) fashion, the resulting signals arebroadened since transverse relaxation rates add up (Kontaxis et al., J.Magn. Reson. 143:184-196 (2004)). This limits the precision ofsimultaneous RDC measurements significantly.

The present invention is directed to overcoming the above-noteddeficiencies in the art.

SUMMARY OF THE INVENTION

The present invention relates to a method of conducting a (5,3)dimensional (D) [HN{N,CO}{C ^(αβ) C ^(α)}] G-matrix Fouriertransformation (GFT) nuclear magnetic resonance (NMR) experiment. (Thisexperiment is also referred to as a “G²FT (5,3) [HN{N,CO}{C ^(αβ) C^(α))}]NMR experiment” throughout this patent application.) The methodinvolves providing a sample, where the sample is a protein moleculehaving two consecutive amino acid residues, i−1 and i, and the chemicalshift values for the following nuclei are measured: (1) α- and β-carbonsof amino acid residues i and i−1, ¹³C^(α/β) _(i/i-1); (2) a polypeptidebackbone amide nitrogen of amino acid residue i, ¹⁵N_(i); (3) apolypeptide backbone carbonyl carbon of amino acid residue i−1,¹³C′_(i-1); and (4) a polypeptide backbone amide proton of amino acidresidue i, ¹H^(N) _(i). Next, radiofrequency pulses for a 5D FT NMRexperiment are applied to the sample. Then, a first set of 2 indirectchemical shift evolution periods of the 5D FT NMR experiment, ¹³C^(α/β)_(i/i-1) and ¹³C^(α) _(i/i-1), is selected. Next, the first set of 2indirect chemical shift evolution periods is jointly sampled in a firstindirect time domain dimension, t₁(¹³C^(α/β) _(i/i-1), ¹³C^(α)_(i/i-1)). Then, a second set of 2 indirect chemical shift evolutionperiods of the 5D FT NMR experiment, ¹⁵N_(i) and ¹³C′_(i-1), isselected. Next, the second set of 2 indirect chemical shift evolutionperiods is jointly sampled in a second indirect time domain dimension,t₂(¹⁵N_(i), ¹³C′_(i-1)). Then, NMR signals detected in a directdimension are independently cosine and sine modulated to generate 3Dbasic NMR spectra containing frequency domain signals having a chemicalshift multiplet with 4 components resulting from each of 2 chemicalshift doublet components in a first frequency domain dimension,ω₁(¹³C^(α/β), ¹³C^(α)), giving rise to 2 chemical shift doubletcomponents in a second frequency domain dimension, ω₂(¹⁵N, ¹³C′),thereby enabling phase-sensitive sampling of all jointly sampled 4indirect chemical shift evolution periods. Finally, the 3D basic NMRspectra are transformed into 3D phase-sensitively edited basic NMRspectra, where the 4 chemical shift multiplet components of the 3D basicNMR spectra are edited to yield 3D phase-sensitively edited basic NMRspectra having individual chemical shift multiplet components.

Another aspect of the present invention relates to a method ofconducting a (5,3) dimensional (D) [HN{NCO}{C ^(αα) C ^(α)}] G-matrixFourier transformation (GFT) nuclear magnetic resonance (NMR)experiment. (This experiment is also referred to as a “G²FT (5,3)[HN{NCO}{C ^(αβ) C ^(α)}]NMR experiment” throughout this patentapplication.) The method involves providing a sample, where the sampleis a protein molecule having two consecutive amino acid residues, i−1and i, and the chemical shift values for the following nuclei aremeasured: (1) α- and β-carbons of amino acid residue i−1, ¹³C^(α/β)_(i-1); (2) a polypeptide backbone amide nitrogen of amino acid residuei, ¹⁵N_(i); (3) a polypeptide backbone carbonyl carbon of amino acidresidue i−1, ¹³C′_(i-1); and (4) a polypeptide backbone amide proton ofamino acid residue i, ¹H^(N) _(i). Next, radio frequency pulses for a 5DFT NMR experiment are applied to the sample. Then, a first set of 2indirect chemical shift evolution periods of the 5D FT NMR experiment,¹³C^(α/β) _(i-1) and ¹³C^(α) _(i-1), is selected. Next, the first set of2 indirect chemical shift evolution periods is jointly sampled in afirst indirect time domain dimension, t₁(¹³C^(α/β) _(i-1), ¹³C^(α)_(i-1)). Then, a second set of 2 indirect chemical shift evolutionperiods of the 5D FT NMR experiment, ¹⁵N_(i) and ¹³C′_(i-1), isselected. Next, the second set of 2 indirect chemical shift evolutionperiods is jointly sampled in a second indirect time domain dimension,t₂(¹⁵N_(i), ¹³C′_(i-1)). Then, NMR signals detected in a directdimension are independently cosine and sine modulated to generate 3Dbasic NMR spectra containing frequency domain signals having a chemicalshift multiplet with 4 components resulting from each of 2 chemicalshift doublet components in a first frequency domain dimension,ω₁(¹³C^(α/β), ¹³C^(α)), giving rise to 2 chemical shift doubletcomponents in a second frequency domain dimension, ω₂(¹⁵N, ¹³C′),thereby enabling phase-sensitive sampling of all jointly sampled 4indirect chemical shift evolution periods. Finally, the 3D basic NMRspectra are transformed into 3D phase-sensitively edited basic NMRspectra, where the 4 chemical shift multiplet components of the 3D basicNMR spectra are edited to yield 3D phase-sensitively edited basic NMRspectra having individual chemical shift multiplet components.

Another aspect of the present invention relates to a method ofconducting a (5,3) dimensional (D) [HN{NC ^(α)}{C ^(αβ) C ^(α)}]G-matrix Fourier transformation (GFT) nuclear magnetic resonance (NMR)experiment. (This experiment is also referred to as a “G²FT (5,3) [HN{NC^(α)}{C ^(αβ)C^(α)}]NMR experiment” throughout this patent application.)The method involves providing a sample, where the sample is a proteinmolecule having two consecutive amino acid residues, i−1 and i, and thechemical shift values for the following nuclei are measured: (1) α- andβ-carbons of amino acid residue i and i−1, ¹³C^(α/β) _(i/i-1); (2) apolypeptide backbone amide nitrogen of amino acid residue i, ¹⁵N_(i);and (3) a polypeptide backbone amide proton of amino acid residue i,¹H^(N) _(i). Next, radiofrequency pulses for a 5D FT NMR experiment areapplied to the sample. Then, a first set of 2 indirect chemical shiftevolution periods of the 5D FT NMR experiment, ¹³C^(α/β) _(i/i-1) and¹³C^(α) _(i/i-1), is selected. Next, the first set of 2 indirectchemical shift evolution periods is jointly sampled in a first indirecttime domain dimension, t₁(¹³C^(α/β) _(i/i-1), ¹³C^(α) _(i/i-1)). Then, asecond set of 2 indirect chemical shift evolution periods of the 5D FTNMR experiment, ¹⁵N_(i) and ¹³C^(α) _(i/i−1), is selected. Next, thesecond set of 2 indirect chemical shift evolution periods is jointlysampled in a second indirect time domain dimension, t₂(¹⁵N_(i), ¹³C^(α)_(i/i-1)). Then, NMR signals detected in a direct dimension areindependently cosine and sine modulated to generate 3D basic NMR spectracontaining frequency domain signals having a chemical shift multipletwith 4 components resulting from each of 2 chemical shift doubletcomponents in a first frequency domain dimension, ω₁(¹³C^(α/β),¹³C^(α)), giving rise to 2 chemical shift doublet components in a secondfrequency domain dimension, ω₂(¹⁵N, ¹³C^(α)), thereby enablingphase-sensitive sampling of all jointly sampled 4 indirect chemicalshift evolution periods. Finally, the 3D basic NMR spectra aretransformed into 3D phase-sensitively edited basic NMR spectra, wherethe 4 chemical shift multiplet components of the 3D basic NMR spectraare edited to yield 3D phase-sensitively edited basic NMR spectra havingindividual chemical shift multiplet components.

Another aspect of the present invention relates to a method ofconducting a (5,3) dimensional (D) [HN{N(CO)C ^(α)}{C ^(αβ) C ^(α)}]G-matrix Fourier transformation (GFT) nuclear magnetic resonance (NMR)experiment. (This experiment is also referred to as a “G²FT (5,3)[HN{N(CO)C ^(α)}{C ^(αβ) C ^(α))}]NMR experiment” throughout this patentapplication.) The method involves providing a sample, where the sampleis a protein molecule having two consecutive amino acid residues, i−1and i, and the chemical shift values for the following nuclei aremeasured: (1) α- and β-carbons of amino acid residue i−1, ¹³C^(α/β)_(i-1); (2) a polypeptide backbone amide nitrogen of amino acid residuei, ¹⁵N_(i); and (3) a polypeptide backbone amide proton of amino acidresidue i, ¹H^(N) _(i). Next, radiofrequency pulses for a 5D FT NMRexperiment are applied to the sample. Then, a first set of 2 indirectchemical shift evolution periods of the 5D FT NMR experiment, ¹³C^(α/β)_(i-1) and ¹³C^(α) _(i-1), is selected. Next, the first set of 2indirect chemical shift evolution periods is jointly sampled in a firstindirect time domain dimension, t₁(¹³C^(α/β) _(i-1), ¹³C^(α) _(i-1)).Then, a second set of 2 indirect chemical shift evolution periods of the5D FT NMR experiment, ¹⁵N_(i) and ¹³C^(α) _(i-1), is selected. Next, thesecond set of 2 indirect chemical shift evolution periods is jointlysampled in a second indirect time domain dimension, t₂(¹⁵N_(i), ¹³C^(α)_(i-1)). Then, NMR signals detected in a direct dimension areindependently cosine and sine modulated to generate 3D basic NMR spectracontaining frequency domain signals having a chemical shift multipletwith 4 components resulting from each of 2 chemical shift doubletcomponents in a first frequency domain dimension, ω₁(¹³C^(α/β),¹³C^(α)), giving rise to 2 chemical shift doublet components in a secondfrequency domain dimension, ω₂(¹⁵N, ¹³C^(α)), thereby enablingphase-sensitive sampling of all jointly sampled 4 indirect chemicalshift evolution periods. Finally, the 3D basic NMR spectra aretransformed into 3D phase-sensitively edited basic NMR spectra, wherethe 4 chemical shift multiplet components of the 3D basic NMR spectraare edited to yield 3D phase-sensitively edited basic NMR spectra havingindividual chemical shift multiplet components.

Another aspect of the present invention relates to a method ofconducting a (5,3) dimensional (D) [HN{N,CO}{C ^(α) H ^(α)}] G-matrixFourier transformation (GFT) nuclear magnetic resonance (NMR)experiment. (This experiment is also referred to as a “G²FT (5,3)[HN{N,CO}{C ^(α) H ^(α)}]NMR experiment” throughout this patentapplication.) The method involves providing a sample, where the sampleis a protein molecule having two consecutive amino acid residues, i−1and i, and the chemical shift values for the following nuclei aremeasured: (1) (α-carbon of amino acid residues i and i−1, ¹³C^(α)_(i/i-1); (2) α-proton of amino acid residues i and i−1, ¹H^(α)_(i/i-1); (3) a polypeptide backbone amide nitrogen of amino acidresidue i, ¹⁵N_(i); (4) a polypeptide backbone carbonyl carbon of aminoacid residue i−1, ¹³C′_(i-1); and (5) a polypeptide backbone amideproton of amino acid residue i, ¹H^(N) _(i). Next, radiofrequency pulsesfor a 5D FT NMR experiment are applied to the sample. Then, a first setof 2 indirect chemical shift evolution periods of the 5D FT NMRexperiment, ¹H^(α) _(i/i-1) and ¹³C^(α) _(i/i-1), is selected. Next, thefirst set of 2 indirect chemical shift evolution periods is jointlysampled in a first indirect time domain dimension, t₁(¹H^(α) _(i/i-1),¹³C^(α) _(i/i-1)). Then, a second set of 2 indirect chemical shiftevolution periods of the 5D FT NMR experiment, ¹⁵N_(i) and ¹³C′_(i-1),is selected. Next, the second set of 2 indirect chemical shift evolutionperiods is jointly sampled in a second indirect time domain dimension,t₂(¹⁵N_(i), ¹³C′_(i-1)). Then, NMR signals detected in a directdimension are independently cosine and sine modulated to generate 3Dbasic NMR spectra containing frequency domain signals having a chemicalshift multiplet with 4 components resulting from each of 2 chemicalshift doublet components in a first frequency domain dimension,ω₁(¹H^(α), ¹³C^(α)), giving rise to 2 chemical shift doublet componentsin a second frequency domain dimension, ω₂(¹⁵N, ¹³C′), thereby enablingphase-sensitive sampling of all jointly sampled 4 indirect chemicalshift evolution periods. Finally, the 3D basic NMR spectra aretransformed into 3D phase-sensitively edited basic NMR spectra, wherethe 4 chemical shift multiplet components of the 3D basic NMR spectraare edited to yield 3D phase-sensitively edited basic NMR spectra havingindividual chemical shift multiplet components.

Another aspect of the present invention relates to a method ofconducting a (5,3) dimensional (D) [{H ^(α) C ^(α)}{CON}HN] G-matrixFourier transformation (GFT) nuclear magnetic resonance (NMR)experiment. (This experiment is also referred to as a “G²FT (5,3) [{H^(α) C ^(α)}{CON}HN]NMR experiment” throughout this patent application.)The method involves providing a sample, where the sample is a proteinmolecule having two consecutive amino acid residues, i−1 and i, and thechemical shift values for the following nuclei are measured: (1)α-carbon of amino acid residue i−1, ¹³C^(α) _(i-1); (2) α-proton ofamino acid residue i−1, ¹H^(α) _(i-1); (3) a polypeptide backbone amidenitrogen of amino acid residue i, ¹⁵N_(i); (4) a polypeptide backbonecarbonyl carbon of amino acid residue i−1, ¹³C′_(i-1); and (5) apolypeptide backbone amide proton of amino acid residue i, ¹H^(N) _(i).Next, radiofrequency pulses for a 5D FT NMR experiment are applied tothe sample. Then, a first set of 2 indirect chemical shift evolutionperiods of the 5D FT NMR experiment, ¹H^(α) _(i-1) and ¹³C^(α) _(i-1),is selected. Next, the first set of 2 indirect chemical shift evolutionperiods is jointly sampled in a first indirect time domain dimension,t₁(¹H^(α) _(i-1), ¹³C^(α) _(i-1)). Then, a second set of 2 indirectchemical shift evolution periods of the 5D FT NMR experiment, ¹⁵N_(i)and ¹³C′_(i-1), is selected. Next, the second set of 2 indirect chemicalshift evolution periods is jointly sampled in a second indirect timedomain dimension, t₂(¹⁵N_(i), ¹³C′_(i-1)). Then, NMR signals detected ina direct dimension are independently cosine and sine modulated togenerate 3D basic NMR spectra containing frequency domain signals havinga chemical shift multiplet with 4 components resulting from each of 2chemical shift doublet components in a first frequency domain dimension,ω₁(¹H^(α), ¹³C^(α)), giving rise to 2 chemical shift doublet componentsin a second frequency domain dimension, ω₂(¹⁵N, ¹³C′), thereby enablingphase-sensitive sampling of all jointly sampled 4 indirect chemicalshift evolution periods. Finally, the 3D basic NMR spectra aretransformed into 3D phase-sensitively edited basic NMR spectra, wherethe 4 chemical shift multiplet components of the 3D basic NMR spectraare edited to yield 3D phase-sensitively edited basic NMR spectra havingindividual chemical shift multiplet components.

Another aspect of the present invention relates to a method ofconducting a (6,3) dimensional (D) [{H ^(αβ) C ^(αβ) C ^(α)}{CON}HN]G-matrix Fourier transformation (GFT) nuclear magnetic resonance (NMR)experiment. (This experiment is also referred to as a “G²FT (6,3) [{H^(αβ) C ^(αβ) C ^(α)}{CON}HN]NMR experiment” throughout this patentapplication.) The method involves providing a sample, where the sampleis a protein molecule having two consecutive amino acid residues, i−1and i, and the chemical shift values for the following nuclei aremeasured: (1) α- and β-carbons of amino acid residue i−1, ¹³C^(α/β)_(i-1); (2) α- and β-protons of amino acid residue i−1, ¹H^(α/β) _(i-1);(3) a polypeptide backbone carbonyl carbon of amino acid residue i−1,¹³C′_(i-1); (4) a polypeptide backbone amide nitrogen of amino acidresidue i, ¹⁵N_(i); and (5) a polypeptide backbone amide proton of aminoacid residue i, ¹H^(N) _(i). Next, radiofrequency pulses for a 6D FT NMRexperiment are applied to the sample. Then, a first group of 3 indirectchemical shift evolution periods of the 6D FT NMR experiment, ¹H^(α/β)_(i-1), ¹³C^(α/β) _(i-1), and ¹³C^(α) _(i-1), is selected. Next, thefirst group of 3 indirect chemical shift evolution periods is jointlysampled in a first indirect time domain dimension, t₁(¹H^(α/β) _(i-1),¹³C^(α/β) _(i-1), ¹³C^(α) _(i-1)). Then, a second group of 2 indirectchemical shift evolution periods of the 6D FT NMR experiment, ¹⁵N_(i)and ¹³C′_(i-1), is selected. Next, the second group of 2 indirectchemical shift evolution periods is jointly sampled in a second indirecttime domain dimension, t₂(¹⁵N_(i), ¹³C′_(i-1)). Then, NMR signalsdetected in a direct dimension are independently cosine and sinemodulated to generate 3D basic NMR spectra containing frequency domainsignals having a chemical shift multiplet with 8 components resultingfrom each of 4 chemical shift doublet components in a first frequencydomain dimension, ω₁(¹³C^(α/β), ¹³C^(α)), giving rise to 2 chemicalshift doublet components in a second frequency domain dimension, ω₂(¹⁵N,¹³C′), thereby enabling phase-sensitive sampling of all jointly sampled5 indirect chemical shift evolution periods. Finally, the 3D basic NMRspectra are transformed into 3D phase-sensitively edited basic NMRspectra, where the 8 chemical shift multiplet components of the 3D basicNMR spectra are edited to yield 3D phase-sensitively edited basic NMRspectra having individual chemical shift multiplet components.

Yet another aspect of the present invention relates to a method ofconducting a (5,3) dimensional (D) [HC(C)C—CH] G-matrix Fouriertransformation (GFT) nuclear magnetic resonance (NMR) experiment. Themethod involves providing a sample, where the sample is a proteinmolecule and the chemical shift values for the following nuclei aremeasured: (1) a proton, ¹H; (2) a carbon coupled to ¹H, ¹³C; (3) acarbon coupled, via another carbon, to ¹³C, ¹³C^(coupled); and (4) aproton coupled to ¹³C^(coupled), ¹H^(coupled), where the chemical shiftof ¹³C^(coupled) provides signal dispersion in an indirect dimension.Next, radiofrequency pulses for a 5D FT NMR experiment are applied tothe sample. Then, 3 indirect chemical shift evolution periods of the 5DFT NMR experiment, ¹H, ¹³C, and ¹³C^(coupled), are selected. Next, the 3indirect chemical shift evolution periods are jointly sampled in anindirect time domain dimension, t₁(¹H,¹³C,¹³C^(coupled)). Then, NMRsignals detected in a direct dimension are independently cosine and sinemodulated to generate 3D basic NMR spectra containing frequency domainsignals with 4 chemical shift multiplet components, thereby enablingphase-sensitive sampling of all jointly sampled 3 indirect chemicalshift evolution periods. Finally, the 3D basic NMR spectra aretransformed into 3D phase-sensitively edited basic NMR spectra, wherethe 4 chemical shift multiplet components of the 3D basic NMR spectraare edited to yield 3D phase-sensitively edited basic NMR spectra havingindividual chemical shift multiplet components.

The present invention also relates to a method of conducting alongitudinal aromatic proton relaxation optimized (4,3) dimensional (D)[HCCH] G-matrix Fourier transformation (GFT) nuclear magnetic resonance(NMR) experiment. The method involves providing a sample, where thesample is a protein molecule and the chemical shift values for thefollowing nuclei are measured: (1) an aromatic proton, ¹H; (2) anaromatic carbon coupled to ¹H, ¹³C; (3) a carbon coupled to ¹³C,¹³C^(coupled); and (4) a proton coupled to ¹³C^(coupled), ¹H^(coupled).Next, radiofrequency pulses for a 4D FT NMR experiment are applied tothe sample, under conditions effective to allow longitudinal relaxationoptimization of the aromatic protons. Then, 2 indirect chemical shiftevolution periods of the 4D FT NMR experiment, ¹H and ¹³C, are selected.Next, the 2 indirect chemical shift evolution periods are jointlysampled in an indirect time domain dimension, t₁(¹H, ¹³C). Then, NMRsignals detected in a direct dimension are independently cosine and sinemodulated to generate 3D basic NMR spectra containing frequency domainsignals with 2 chemical shift doublet components, thereby enablingphase-sensitive sampling of the jointly sampled 2 indirect chemicalshift evolution periods. Finally, the 3D basic NMR spectra aretransformed into 3D phase-sensitively edited basic NMR spectra, wherethe 2 chemical shift doublet components of the 3D basic NMR spectra areedited to yield 3D phase-sensitively edited basic NMR spectra havingindividual chemical shift doublet components.

Another aspect of the present invention relates to a method ofconducting a longitudinal aromatic proton relaxation optimized (4,3)dimensional (D) [HCCH] G-matrix Fourier transformation (GFT) nuclearmagnetic resonance (NMR) experiment. The method involves providing asample, where the sample is a protein molecule and the chemical shiftvalues for the following nuclei are measured: (1) an aromatic proton,¹H; (2) an aromatic carbon coupled to ¹H, ¹³C; (3) a carbon coupled to¹³C, ¹³C^(coupled); and (4) a proton coupled to ¹³C^(coupled),¹H^(coupled). Next, radiofrequency pulses for a 4D FT NMR experiment areapplied to the sample under conditions effective to allow longitudinalrelaxation optimization of the aromatic protons. Then, 2 indirectchemical shift evolution periods of the 4D FT NMR experiment, ¹³C and¹³C^(coupled), are selected. Next, the 2 indirect chemical shiftevolution periods are jointly sampled in an indirect time domaindimension, t₁(¹³C, ¹³C^(coupled)). Then, NMR signals detected in adirect dimension are independently cosine and sine modulated to generate3D basic NMR spectra containing frequency domain signals with 2 chemicalshift doublet components, thereby enabling phase-sensitive sampling ofthe jointly sampled 2 indirect chemical shift evolution periods.Finally, the 3D basic NMR spectra are transformed into 3Dphase-sensitively edited basic NMR spectra, where the 2 chemical shiftdoublet components of the 3D basic NMR spectra are edited to yield 3Dphase-sensitively edited basic NMR spectra having individual chemicalshift doublet components.

Another aspect of the present invention relates to a method ofconducting a longitudinal aromatic proton relaxation optimized (4,3)dimensional (D) [HCCH] G-matrix Fourier transformation (GFT) nuclearmagnetic resonance (NMR) experiment. The method involves providing asample, where the sample is a protein molecule and the chemical shiftvalues for the following nuclei are measured: (1) an aromatic proton,¹H; (2) an aromatic carbon coupled to ¹H, ¹³C; (3) a carbon coupled to¹³C, ¹³C^(coupled); and (4) a proton coupled to ¹³C^(coupled),¹H^(coupled). Next, radiofrequency pulses for a 4D FT NMR experiment areapplied to the sample under conditions effective to allow longitudinalrelaxation optimization of the aromatic protons. Then, 2 indirectchemical shift evolution periods of the 4D FT NMR experiment, ¹H and¹³C^(coupled), are selected. Next, the 2 indirect chemical shiftevolution periods are jointly sampled in an indirect time domaindimension, t₁(¹H, ¹³C^(coupled)). Then, NMR signals detected in a directdimension are independently cosine and sine modulated to generate 3Dbasic NMR spectra containing frequency domain signals with 2 chemicalshift doublet components, thereby enabling phase-sensitive sampling ofthe jointly sampled 2 indirect chemical shift evolution periods.Finally, the 3D basic NMR spectra are transformed into 3Dphase-sensitively edited basic NMR spectra, where the 2 chemical shiftdoublet components of the 3D basic NMR spectra are edited to yield 3Dphase-sensitively edited basic NMR spectra having individual chemicalshift doublet components.

In addition, the present invention relates to a method of conducting a(3,2) dimensional (D) <[¹ H ^(X) X]-nuclear Overhauser enhancementspectroscopy (NOESY)-[¹H]> G-matrix Fourier transformation (GFT) nuclearmagnetic resonance (NMR) experiment. The method involves providing asample, where the sample is a protein molecule and the chemical shiftvalues for the following nuclei are measured: (1) a proton, ¹H; (2) X,where X is an aliphatic carbon, ¹³C^(ali), an aromatic carbon,¹³C^(aro), or a nitrogen, ¹⁵N; and (3) a proton bound to X, ¹H^(X).Next, radiofrequency pulses for a first 3D NOESY FT NMR experiment areapplied to the sample. Then, a first set of 2 indirect chemical shiftevolution periods of the 3D NOESY FT NMR experiment, ¹H^(X) and X, isjointly sampled in an indirect time domain dimension, t₁(¹H^(X),X).Next, NMR signals detected in a direct dimension are independentlycosine and sine modulated to generate 2D basic NMR spectra containingfrequency domain signals with 2 chemical shift doublet components,thereby enabling phase-sensitive sampling of the jointly sampled firstset of 2 indirect chemical shift evolution periods. Finally, the 2Dbasic NMR spectra are transformed into 2D phase-sensitively edited basicNMR spectra, where the 2 chemical shift doublet components of the 2Dbasic NMR spectra are edited to yield 2D phase-sensitively edited basicNMR spectra having individual chemical shift doublet components.

Another aspect of the present invention relates to a method ofconducting a (4,3) dimensional (D) <[¹ H ^(X) X]-nuclear Overhauserenhancement spectroscopy (NOESY)-[Y¹H^(Y)]> G-matrix Fouriertransformation (GFT) nuclear magnetic resonance (NMR) experiment. Themethod involves providing a sample, where the sample is a proteinmolecule and the chemical shift values for the following nuclei aremeasured: (1) X, where X is an aliphatic carbon, ¹³C^(ali), an aromaticcarbon, ¹³C^(aro), or a nitrogen, ¹⁵N; (2) a proton bound to X, ¹H^(X);(3) Y, where Y is an aliphatic carbon, ¹³C^(ali), an aromatic carbon,¹³C^(aro), or a nitrogen, ¹⁵N; and (4) a proton bound to Y, ¹H^(Y).Next, radiofrequency pulses for a first 4D NOESY FT NMR experiment areapplied to the sample. Then, a first set of 2 indirect chemical shiftevolution periods of the 4D NOESY FT NMR experiment, ¹H^(X) and X, isselected. Next, the first set of 2 indirect chemical shift evolutionperiods is jointly sampled in an indirect time domain dimension,t₁(¹H^(X),X). Then, NMR signals detected in a direct dimension areindependently cosine and sine modulated to generate 3D basic NMR spectracontaining frequency domain signals with 2 chemical shift doubletcomponents, thereby enabling phase-sensitive sampling of the jointlysampled 2 indirect chemical shift evolution periods. Finally, the 3Dbasic NMR spectra are transformed into 3D phase-sensitively edited basicNMR spectra, where the 2 chemical shift doublet components of the 3Dbasic NMR spectra are edited to yield 3D phase-sensitively edited basicNMR spectra having individual chemical shift doublet components.

Another aspect of the present invention relates to a method ofconducting a (4,2) dimensional (D) <[¹ H ^(X) X]-nuclear Overhauserenhancement spectroscopy (NOESY)-[Y ¹H^(Y)]> G-matrix Fouriertransformation (GFT) nuclear magnetic resonance (NMR) experiment. Themethod involves providing a sample, where the sample is a proteinmolecule and the chemical shift values for the following nuclei aremeasured: (1) X, where X is an aliphatic carbon, ¹³C^(ali), an aromaticcarbon, ¹³C^(aro), or a nitrogen, ¹⁵N; (2) a proton bound to X, ¹H^(X);(3) Y, where Y is an aliphatic carbon, ¹³C^(ali), an aromatic carbon,¹³C^(aro), or a nitrogen, ¹⁵N; and (4) a proton bound to Y, ¹H^(Y).Next, radiofrequency pulses for a first 4D NOESY FT NMR experiment areapplied to the sample. Then, a first group of 3 indirect chemical shiftevolution periods of the 4D NOESY FT NMR experiment, ¹H^(X), X, and Y,is selected. Next, the first group of 3 indirect chemical shiftevolution periods is jointly sampled in an indirect time domaindimension, t₁(¹H^(X),X,Y). Then, NMR signals detected in a directdimension are independently cosine and sine modulated to generate 2Dbasic NMR spectra containing frequency domain signals with 4 chemicalshift multiplet components, thereby enabling phase-sensitive sampling ofall jointly sampled 3 indirect chemical shift evolution periods.Finally, the 2D basic NMR spectra are transformed into 2Dphase-sensitively edited basic NMR spectra, where the 4 chemical shiftmultiplet components of the 2D basic NMR spectra are edited to yield 2Dphase-sensitively edited basic NMR spectra having individual chemicalshift multiplet components.

The present invention also relates to a method of conducting a (6,2)dimensional (D) [(H^(α)—C^(α)—CO)—N—HN] G-matrix Fourier transformation(GFT) nuclear magnetic resonance (NMR) experiment. The method involvesproviding a sample, where the sample is a protein molecule having twoconsecutive amino acid residues, i-1 and i, and the chemical shiftvalues for the following nuclei: (1) a polypeptide backbone amidenitrogen of amino acid residue i, ¹⁵N_(i); and (2) a polypeptidebackbone amide proton of amino acid residue i, ¹H^(N) _(i), are measuredin combination with four spin-spin couplings between (1) an α-proton ofamino acid residue i−1, ¹H^(α) _(i-1), and an α-carbon of amino acidresidue i−1, ¹³C^(α) _(i-1); (2) an α-carbon of amino acid residue i−1,¹³C^(α) _(i-1), and a polypeptide backbone carbonyl carbon of amino acidresidue i−1, ¹³C′_(i-1); (3) a polypeptide backbone carbonyl carbon ofamino acid residue i−1, ¹³C′_(i-1), and a polypeptide backbone amidenitrogen of amino acid residue i, ¹⁵N_(i); (4) a polypeptide backboneamide nitrogen of amino acid residue i, ¹⁵N_(i), and a polypeptidebackbone amide proton of amino acid residue i, ¹H^(N) _(i). Next,radiofrequency pulses for a 6D FT NMR experiment are applied to thesample. Then, an indirect chemical shift evolution period of the 6D FTNMR experiment, ¹⁵N_(i), is selected. Next, the indirect chemical shiftevolution period is jointly sampled with the four indirect spin-spincoupling evolution periods resulting from sampling the four spin-spincouplings. Then, NMR signals detected in a direct dimension resultingfrom time evolution of the indirect chemical shift and the fourspin-spin couplings are independently cosine and sine modulated togenerate 2D basic NMR spectra containing frequency domain signals with16 multiplet components, thereby enabling phase-sensitive sampling ofthe indirect chemical shift evolution period and the indirect spin-spincoupling evolution periods. Finally, the 2D basic NMR spectra aretransformed into 2D phase-sensitively edited basic NMR spectra, wherethe 16 multiplet components of the 2D basic NMR spectra are edited toyield 2D phase-sensitively edited basic NMR spectra having individualmultiplet components.

Previously described GFT NMR experiments comprised phase sensitive jointsampling of several chemical shifts along a single indirect dimension(also called as the “GFT dimension”) of a multidimensional NMRexperiment, thereby providing high spectral dispersion. However, inlarge proteins, spectral overlap can still hamper resonance assignments.The present invention alleviates this problem by additionally employinganother indirect dimension as a second GFT dimension, resulting insignificant gains in spectral resolution. The phase sensitive jointsampling of two independent sets of spins along two indirect dimensionsrequires the sequential application of two appropriate G-matrixtransformations along each of the GFT dimensions independently; hence,these are called G²FT NMR experiments. The present application disclosesa suite of novel (5,3)D and (6,3)D G²FT triple resonance NMR experimentsencoding highly resolved 5D and 6D spectral information for sequentialresonance assignment of proteins exhibiting high chemical shiftdegeneracy. Efficient resonance assignment is achieved by separate jointsampling of (i) chemical shifts which solely serve to provide increasedresolution and (ii) shifts which also provide sequential connectivities.In the (5,3)D G²FT experiments, for example, two G-matrixtransformations are employed. Peaks are resolved along a first GFTdimension at both Ω(¹⁵N)+Ω(¹³C′) and Ω(¹⁵N)−Ω(¹³C′), or atΩ(¹⁵N)+Ω(¹³C^(α)) and Ω(¹⁵N)−Ω(¹³C^(α)), in order to break backbone¹⁵N,¹H^(N) chemical shift degeneracy. Sequential connectivities areestablished along a second GFT dimension by measuring intraresidue andsequential correlations at 2 Ω(¹³C^(α)), Ω(¹³C^(α)+¹³C^(β)) andΩ(¹³C^(α)−¹³C^(β)), or at Ω(¹³C^(α)+¹H^(α)) and Ω(¹³C^(α)−¹H^(α)), inorder to resolve ¹³C^(α/β), ¹H^(α) chemical shift degeneracy. Thepresent invention demonstrates that longitudinal proton relaxationoptimization of out-and-back implementations suitable for deuteratedproteins, and non-linear data sampling combined with maximum entropyreconstruction further accelerate G²FT NMR data acquisition speed. As aresult, the spectral information can be obtained within hours, so that(5,3)D G²FT experiments are viable options for high-throughput structuredetermination in structural genomics. Applications are also presentedfor 17 kDa α-helical protein YqbG and 13.5 kDa protein rps24e, targetsof the Northeast Structural Genomics consortium, as well as for 9 kDaprotein Z-domain. The high resolving power of the G²FT NMR experimentsmakes them attractive choices to study α-helical globular/membrane or(partially) unfolded proteins, thus promising to pave the way forNMR-based structural genomics of membrane proteins.

In addition, NMR assignment of aromatic rings in proteins is aprerequisite for obtaining high-quality solution structures of proteinsand for studying the dynamics and folding of their molecular cores. Thepresent application discloses sensitive PFG-PEP L-GFT-(TROSY) (4,3)DHCCH NMR (as well as other L-GFT (4,3) NMR experiments) foridentification of aromatic spin systems based on 4D spectral informationwhich can be rapidly obtained with high digital resolution. The GFTexperiment relies on newly introduced longitudinal relaxation(L-)optimization for aromatic protons and is optimally suited for bothsensitivity and sampling limited data collection, making it particularlyattractive for NMR-based structural genomics. L-GFT (4,3)D HCCH offers˜25% higher intrinsic sensitivity at optimal relaxation delay betweenscans for medium-sized proteins when compared with the non-L congener.L-GFT (4,3)D HCCH also allows one to collect the 4D spectral informationabout four times faster (due to the ability to acquire data with fourtimes shorter relaxation delays between scans), while the same intrinsicsensitivity (sensitivity per unit time) is observed as for the non-Lcongener at optimal relaxation delays between scans. Applications arealso presented for 21 kDa and 13 kDa proteins, HR41 and MaR11, targetsof the Northeast Structural Genomics Consortium for which datacollection is, respectively, sensitivity and sampling limited. Completeassignment of aromatic rings enabled high-quality NMR structuredetermination, and nearly complete analysis of aromatic protonlinewidths allowed one to assess the flipping of most rings in HR41.Specifically, the ring of Tyr 90 flips very slowly on the seconds timescale, thereby proving the absence of fast larger amplitude motionalmodes which could allow the ring to flip. This indicates remarkablerigidity of the substructure in which the ring is embedded. Tyr 90 isconserved among ubiquitin-conjugating enzymes E2 to which HR41 belongs,and is located in spatial proximity to the interface between E2 andubiquitin-protein ligase E3. Hence, the conformational rigidity and/orthe slow motional mode probed by the ring might be of functionalimportance.

In addition, the present application discloses a protocol forhigh-quality structure determination based on GFT NMR and NOESY. Fivethrough-bond chemical shift correlation experiments providing 4D and 5Dspectral information at high digital resolution are performed forresonance assignment. These are combined with a newly implemented (4,3)DGFT NOESY experiment which encodes information of 4D ¹⁵N/¹⁵N-,¹³C^(alipahtic)/¹⁵N-, and ¹³C^(aliphatic)/¹³C^(aliphatic)-resolved[¹H,¹H]-NOESY in two subspectra, each containing one component ofchemical shift doublets arising from 4D→3D projection at ω₁:Ω(¹H)±Ω(X)[X=¹⁵N,¹³C^(aliphatic)]. The peaks located at the centers of thedoublets are obtained from simultaneous 3D¹⁵N/¹³C^(aliphatic)/¹³C^(aromatic)-resolved [¹H,¹H]-NOESY, where NOEsdetected on aromatic protons are also obtained. The protocol was appliedfor determining a high-quality structure of the 14 kDa NortheastStructural Genomics consortium target protein, YqfB (PDB ID 1TE7).Through-bond correlation and NOESY spectra were acquired, respectively,in 16.9 hours and 39 hours (30 hours for shift doublets, 9 hours forcentral peaks) on a 600 MHz spectrometer equipped with a cryogenicprobe. The rapidly collected highly resolved 4D NOESY information allowsone to assign the majority of NOEs directly from chemical shifts, whichyields accurate initial structures “within” ˜2 Å to the final structure.Information theoretical “QUEEN” analysis of initial distance limitconstraint networks revealed that, in contrast to structure-basedprotocols, such NOE assignment is not biased toward identifyingadditional constraints that tend to be redundant with respect to theavailable constraint network. The protocol enables rapid NMR datacollection for robust high-quality structure determination of proteinsup to ˜20-25 kDa in high-throughput.

Lastly, in recent years, residual dipolar couplings (RDC) inbiomolecular systems have emerged as a subject of widespread interest inNMR based structural biology and genomics. In all the applications, theimportance of the number and different types of RDCs that are measuredand their accuracy/precision has been recognized. An additional aspectthat is being increasingly considered vital is the simultaneousmeasurement of different types of RDCs. The present applicationdiscloses a novel scheme for simultaneous and precise measurement ofmultiple RDCs in a protein within a single experiment, which is based onthe principle of GFT NMR spectroscopy. Analogues to phase sensitivejoint sampling of chemical shifts, multiple scalar/dipolar couplings arejointly detected in a single dimension. Four mutually correlatedone-bond couplings, namely, ¹³C^(α)—¹H^(α), ¹³C^(α)—¹³C′, ¹⁵N—¹³C′ and¹⁵N—¹H^(N) are simultaneously measured in conjunction with ¹⁵N and¹H^(N) chemical shifts. This experiment is named “J-GFT (6,2)D[(H^(α)—C^(α)—CO)—N—HN]”. The existing delays in the pulse scheme areutilized for joint sampling of couplings in a constant-time fashion,thereby avoiding loss of resolution and sensitivity. Accuracy and highprecision of the RDCs obtained were experimentally verified for Z-domainat two different field strengths. Such mutually correlated sets of RDCsare invaluable as an aid to resonance assignments, studying proteindynamics or in protein structure refinement/validation.

BRIEF DESCRIPTION OF THE DRAWINGS

The patent or application file contains at least one drawing executed incolor. Copies of this patent or patent application publication withcolor drawings will be provided by the U.S. Patent and Trademark Officeupon request and payment of the necessary fee.

FIG. 1(a) illustrates ¹³C′_(i-1),¹⁵N,¹H^(N)-resolved (5,3)D G²FT NMR.FIG. 1(b) illustrates magnetization transfers of HN{N,CO}{C ^(αβ) C^(α)} (left) and HN{NCO}{C ^(αβ) C ^(α)} (right). Double-arrows indicatebidirectional transfers via one-bond scalar couplings. The“intraresidue” experiment (left) also yields sequential connectivitiesvia smaller (Cavanagh et al., Protein NMR Spectroscopy Academic Press:San Diego (1996), which is hereby incorporated by reference in itsentirety) two-bond J_(CN) couplings.

FIG. 2 shows composite plots of [ω₁(¹³C^(α); ¹³C^(αβ)), ω₃(¹H^(N))]strips taken from the basic spectra of G²FT (5,3)D HN{N,CO}{C ^(αβ) C^(α)}. The four basic spectra are grouped into two sets, B1 and B2,comprising peaks at Ω₀(¹⁵N_(i))+Ω₁(¹³C′_(i-1)) andΩ₀(¹⁵N_(i))-Ω₁(¹³C′_(i-1)) along ω₂, respectively. B1 and B2 eachcontain two spectra (labeled as “b1” and “b2”) comprising peaks atω₀(¹³C^(α) _(i/i-1))±Ω₁(¹³C^(α/β) _(i/i-1)) along ω₁. Positive andnegative peaks are shown, respectively, with solid and dotted contourlines. As an example, strips are shown for the residue Val 5 of the 8.6kDa protein Ubiquitin. Peaks labeled 1-4 in “b1” and 5-8 in “b2”correspond to the following linear combination of chemical shifts alongω₁:

(i=Val 5; i−1=Phe 4)

-   -   1. Ω₀(¹³C^(α) _(i))+Ω₁(¹³C^(α) _(i))    -   2. Ω₀(¹³C^(α) _(i-1))+Ω₁(¹³C^(α) _(i-1))    -   3. Ω₀(¹³C^(α) _(i-1))+Ω₁(¹³C^(β) _(i-1))    -   4. Ω₀(¹³C^(α) _(i))+Ω₁(¹³C^(β) _(i))    -   5. Ω₀(¹³C^(α) _(i))−Ω₁(¹³C^(α) _(i))    -   6. Ω₀(¹³C^(α) _(i-1))−Ω₁(¹³C^(α) _(i-1))    -   7. Ω₀(¹³C^(α) _(i-1))−Ω₁(¹³C^(β) _(i-1))    -   8. Ω₀(¹³C^(α) _(i))−Ω₁(¹³C^(β) _(i))

FIG. 3 shows composite plots of [ω₁(¹³C^(α); ¹³C^(αβ)), ω₃(¹H^(N))]strips taken from the basic spectra of G²FT (5,3)D HN{NCO}{C ^(αβ) C^(α)}. The four basic spectra are grouped into two sets, B1 and B2,comprising peaks at Ω₀(¹⁵N_(i))+Ω₁(¹³C′_(i-1)) andΩ₀(¹⁵N_(i))−Ω₁(¹³C′_(i-1)) along ω₂, respectively. B1 and B2 eachcontain two spectra (labeled as “b1” and “b2”) comprising peaks atΩ₀(¹³C^(α) _(i-1))±Ω₁(¹³C^(α/β) _(i-1)) along ω₁. Positive and negativepeaks are shown, respectively, with solid and dotted contour lines. Asan example, strips are shown for the residue Ala 55 of the 8 kDa proteinZ-domain. Peaks labeled 1-2 in “b1” and 3-4 in “b2” correspond to thefollowing linear combination of chemical shifts along ω₁:

-   -   1. Ω₀(¹³C^(α) _(i-1))+Ω₁(¹³C^(α) _(i-1))    -   2. Ω₀(¹³C^(α) _(i-1))+Ω₁(13C^(β) _(i-1))    -   3. Ω₀(¹³C^(α) _(i-1))−Ω₁(13C^(β) _(i-1))    -   4. Ω₀(¹³C^(α) _(i-1))−Ω₁(13C^(α) _(i-1))

FIG. 4 shows composite plots of [ω₁(¹³C^(α); ¹³C^(αβ)), ω₃(¹H^(N))]strips taken from the basic spectra of G²FT (5,3)D {C ^(αβ) C^(α)}{NCO}HN. The four basic spectra are grouped into two sets, B1 andB2, comprising peaks at Ω₀(¹⁵N_(i))+Ω₁(¹³C′_(i-1)) andΩ₀(¹⁵N_(i))−Ω₁(¹³C′_(i-1)) along ω₁, respectively. B1 and B2 eachcontain two spectra (labeled as “b1” and “b2”) comprising peaks atΩ₀(¹³C^(α) _(i-1))±Ω₁(¹³C^(α/β) _(i-1)) along ω₁. As an example, stripsare shown for the residue Ala 46 of Ubiquitin. Peaks labeled 1-4 in “b1”and “b2” correspond to the following linear combination of chemicalshifts along ω₁:

-   -   1. Ω₀(¹³C^(α) _(i-1))+Ω₁(¹³C^(α) _(i-1))    -   2. Ω₀(¹³C^(α) _(i-1))+Ω₁(¹³C^(β) _(i-1))    -   3. Ω₀(¹³C^(α) _(i-1))−Ω₁(¹³C^(β) _(i-1))    -   4. Ω₀(¹³C^(α) _(i-1))−Ω₁(¹³C^(α) _(i-1))

FIG. 5 depicts the r.f. pulse scheme of G²FT L-(5,3)D HN{N,CO}{C ^(αβ) C^(α)}. Rectangular 90° and 180° pulses are indicated by thin and thickvertical bars, respectively, and phases are indicated above the pulses.Where no r.f. phase is marked, the pulse is applied along x. High-power90° pulse lengths are: 5.7 μs for ¹H, 15.0 μs for ¹³C and 40 μs for ¹⁵N,and κ=0.25. The scaling (Kim et al., J. Am. Chem. Soc. 125:1385-1393(2003); Szyperski et al., J. Am. Chem. Soc. 115:9307-9308 (1993), whichare hereby incorporated by reference in their entirety) factor κ for¹³C′ shift evolution was set to 0.25, because (i) polarization transferin the sequential counterpart (i.e. (5,3)D HN{NCO}{C ^(αβ) C ^(α)}(FIGS. 1 and 6)) limits t_(max)(¹³C′) to ˜6 ms; (ii) a shortt_(max)(¹³C′) limits T₂(¹³C′) losses in (5,3)D HN{N,CO}{C ^(αβ) C ^(α)}with non-constant time (Cavanagh et al., Protein NMR SpectroscopyAcademic Press: San Diego (1996), which is hereby incorporated byreference in its entirety) ¹³C′ shift evolution; (iii) t_(max)(¹⁵N) ˜24ms ensures high spectral resolution in ω₂. Lengths of 90° and 180° pulseapplied to ¹³C^(αβ) are set to 48 μs and 43 μs, respectively (at a ¹Hresonance frequency of 600 MHz), prior to and during the first t₁ delay[t₁(¹³C^(αβ))], and to 54 μs and 48 μs, respectively, during the secondt₁ delay [t₁(¹³C^(α))] in order to minimize perturbation of ¹³C′ spins.A 90° E-BURP2 pulse (Geen et al., J. Magn. Reson., 93:93-142 (1991),which is hereby incorporated by reference in its entirety) after the2^(nd) 90° ¹H pulse (1.2 ms; 0-6 ppm excitation; carrier: 3 ppm) enableswater flip-back (Cavanagh et al., Protein NMR Spectroscopy AcademicPress: San Diego (1996), which is hereby incorporated by reference inits entirety) and L-optimization (Atreya et al., Proc. Natl. Acad. Sci.USA 101;9642-9647 (2004); Pervushin et al., J. Am. Chem. Soc.124:12898-12902 (2002), which are hereby incorporated by reference intheir entirety). SEDUCE (Cavanagh et al., Protein NMR SpectroscopyAcademic Press: San Diego (1996), which is hereby incorporated byreference in its entirety) off-resonance 180° pulses of duration 200 μsand 103 μs, respectively, are used to decouple ¹³C′ during t₁(¹³C^(αβ))and t₁(¹³C^(α)). A six-pulse composite sequence (Shaka, Chem. Phy.Lett., 120:201-205 (1985), which is hereby incorporated by reference inits entirety) is used to simultaneously invert/refocus ¹³C^(α)/¹³C′magnetization during ¹³C^(α)—¹³C′ polarization transfers. The SEDUCE(Cavanagh et al., Protein NMR Spectroscopy Academic Press: San Diego(1996), which is hereby incorporated by reference in its entirety)sequence is used for decoupling of ¹³C^(α) during t₂(¹⁵N). WALTZ16(Cavanagh et al., Protein NMR Spectroscopy Academic Press: San Diego(1996), which is hereby incorporated by reference in its entirety) isemployed to decouple of ¹⁵N (r.f.=1.70 kHz) during acquisition. The ¹Hr.f. carrier is placed at the position of the solvent line at 4.77 ppm.The ¹⁵N carrier position is set to 118.5 ppm. The ¹³C carrier positionis set initially to 56 ppm and switched to 175 ppm before the first 90°pulse in ¹³CO. It is switched to 43 ppm prior to and during t₁(¹³C^(αβ))and back to 56 ppm during t₁(¹³C^(α)) (indicated by an arrow). Theduration and strengths of the pulsed rectangular z-field gradients(PFGs) are: G₁(1.0 ms, 24 G/cm); G₂(0.5 ms, 8 G/cm); G₃(1.0 ms, 20G/cm); G₄(0.5 ms, 4 G/cm); G₅(1.0 ms, 15 G/cm); G₆(1.25 ms, 30 G/cm);G₇(0.5 ms, 8 G/cm); G₈(0.125 ms, 29.5 G/cm). Delays: τ₁=5.5 ms; τ₂=5.4;τ₃=τ₄=28; τ₅=4.6; τ₆=1.0; τ_(a)=7.0. Phase cycling: φ₁=x,−x; φ₂=x; φ₃=y;φ₄=2(x),2(−x); φ₅=4(x), 4(−x); φ₆=x; φ₇(receiver)=x,2(−x),x. Asensitivity enhancement scheme (Kay et al., J. Am Chem. Soc.114:10663-10665 (1992), which is hereby incorporated by reference in itsentirety) is employed, i.e., the sign of G6 is inverted in concert witha 180° shift of φ₆. Quadrature detection in t₁(¹³C^(α)) is accomplishedby altering the phases φ₄ according to States-TPPI (Cavanagh et al.,Protein NMR Spectroscopy Academic Press: San Diego (1996), which ishereby incorporated by reference in its entirety), whereas quadraturedetection in t₂(¹⁵N) is achieved by use of the sensitivity enhancementscheme. GFT NMR phase-cycle: φ₁=x,y; φ₂=2x,2y; φ₃=2y,2x, yielding, inconjunction with quadrature detection, 16 data sets which are linearlycombined employing a G-matrix transformation with the G-matrix ofEquation 10 (see Detailed Description of the Invention section).

FIG. 6 depicts the r.f. pulse scheme of G²FT L-(5,3)D HN{NCO}{C ^(αβ) C^(α)}. Rectangular 90° and 180° pulses are indicated by thin and thickvertical bars, respectively, and phases are indicated above the pulses.Where no r.f. phase is marked, the pulse is applied along x. High-power90° pulse lengths are: 5.7 μs for ¹H, 15.0 μs for ¹³C and 40 μs for ¹⁵N,and κ=0.25. Lengths of 90° and 180° pulse applied to ¹³C^(αβ) are set to48 μs and 43 μs, respectively (at a ¹H resonance frequency of 600 MHz),prior to and during the first t₁ delay [t₁(¹³C^(αβ))], and to 54 μs and48 μs, respectively, during the second t₁ delay [t₁(¹³C^(α))] in orderto minimize perturbation of ¹³C′ spins. A 90° E-BURP2 pulse (Geen etal., J. Magn. Reson., 93:93-142 (1991), which is hereby incorporated byreference in its entirety) after the 2^(nd) 90° ¹H pulse (1.2 ms; 0-6ppm excitation; carrier: 3 ppm) enables water flip-back (Cavanagh etal., Protein NMR Spectroscopy Academic Press: San Diego (1996), which ishereby incorporated by reference in its entirety) and L-optimization(Atreya et al., Proc. Natl. Acad. Sci. USA 101:9642-9647 (2004);Pervushin et al., J. Am. Chem. Soc. 124:12898-12902 (2002), which arehereby incorporated by reference in their entirety). SEDUCE (Cavanagh etal., Protein NMR Spectroscopy Academic Press: San Diego (1996), which ishereby incorporated by reference in its entirety) off-resonance 180°pulses of duration 200 μs and 103 μs, respectively, are used to decouple¹³C′ during t₁(¹³C^(αβ)) and t₁(¹³C^(α)). The 90° and 180° pulse lengthsfor the sinc lobe pulse on-resonance at ¹³C′ is 88 μs and 81 μs,respectively. A six-pulse composite sequence (Shaka, Chem. Phy. Lett.,120:201-205 (1985), which is hereby incorporated by reference in itsentirety) is used to simultaneously invert/refocus ¹³C^(α)/¹³C′magnetization during ¹³C^(α)—¹³C′ polarization transfers. The SEDUCE(Cavanagh et al., Protein NMR Spectroscopy, Academic Press: San Diego(1996), which is hereby incorporated by reference in its entirety)sequence is used for decoupling of ¹³C^(α) during t₂(¹⁵N). WALTZ16(Cavanagh et al., Protein NMR Spectroscopy, Academic Press: San Diego(1996), which is hereby incorporated by reference in its entirety) isemployed to decouple of ¹⁵N (r.f.=1.70 kHz) during acquisition. The ¹Hr.f. carrier is placed at the position of the solvent line at 4.77 ppm.The ¹⁵N carrier position is set to 118.5 ppm. The ¹³C carrier positionis set initially to 175 ppm, and switched to 43 ppm prior to and duringt₁(¹³C^(αβ)) (indicated by an arrow at point a), to 56 ppm duringt₁(¹³C^(α)) (at b) and back to 175 ppm (at c) during the reverse¹³C′—¹³C^(α) polarization transfer. The duration and strengths of thepulsed rectangular z-field gradients (PFGs) are: G1 (1.0 ms, 24 G/cm);G2 (0.5 ms, 8 G/cm); G3 (1.0 ms, 20 G/cm); G4 (0.5 ms, 8 G/cm); G5 (1.0ms, 20 G/cm); G6 (0.5 ms, 8 G/cm); G7 (1.25 ms, 30 G/cm); G8 (0.5 ms, 4G/cm); G9 (0.125 ms, 29.5 G/cm). The delays are: τ₁=5.4 ms, τ₂=5.4 ms,τ₃=24 ms, τ₄=24 ms, τ₅=4.6 ms, τ₆=1.0 ms, τ_(a)=9.0 ms, τ_(b)=7.0 ms.Phase cycling: φ₁=x, −x; φ₂=y; φ₃=2(x),2(−x); φ₄=x, φ₅=2(x), 2(−x);φ₆=x; φ₇(receiver)=x, −x, −x, x. A sensitivity enhancement scheme (Kayet al., J. Am. Chem. Soc. 114:10663-10665 (1992), which is herebyincorporated by reference in its entirety) is employed, i.e., the signof G7 is inverted in concert with a 180° shift of φ₆. Quadraturedetection in t₁(¹³C^(α)) is accomplished by altering the phases φ₃according to States-TPPI (Cavanagh et al., Protein NMR SpectroscopyAcademic Press: San Diego (1996), which is hereby incorporated byreference in its entirety), whereas quadrature detection in t₂(¹⁵N) isachieved by use of the sensitivity enhancement scheme. GFT NMRphase-cycle: φ₁=x, y; φ₂=y, x; φ₄=2x, 2y, yielding, in conjunction withquadrature detection, 16 data sets which are linearly combined employinga G-matrix transformation with the G-matrix of Equation 10 (see DetailedDescription of the Invention section).

FIGS. 7(a)-(d) show contour plots of spectra recorded for 17 kDa proteinyqbG on Varian INOVA 600 spectrometer equipped with a cryogenic probe.FIG. 7(a) shows a plot of 2D [¹⁵N—¹H^(N)] HSQC; FIG. 7(b) shows a plotof [ω₂(¹⁵N),ω₃(¹H^(N))]-projection of GFT (4,3)D HNNC ^(αβ) C ^(α) alongω₁(¹³C^(α);¹³C^(αβ)); FIG. 7(c) shows a plot of[ω₂(¹⁵N;¹³C′),ω₃(¹H^(N))]-projection of G²FT L-(5,3)D HN{N,CO}C ^(αβ) C^(α) along ω₁(¹³C^(α);¹³C^(αβ)) comprising peaks at ω₂:Ω(¹⁵N)+κ*Ω(¹³C′);and FIG. 7(d) shows a plot of [ω₂(¹⁵N;¹³C′),ω₃(¹H^(N))]-projection ofG²FT L-(5,3)D HN{N,CO}C ^(αβ) C ^(α) along ω₁(¹³C^(α);¹³C^(αβ))comprising peaks at ω₁:Ω(¹⁵N)−κ*Ω(¹³C′) (κ=0.25). 2D [¹⁵N—¹H^(N)] HSQCwas acquired with t_(2max)(¹⁵N)=80 ms (Table 1), whereast_(2max)(¹⁵N)=24.0 ms for the projections (Table 1). Spectral resolutionof the projections was enhanced by linear prediction (Cavanagh et al.,Protein NMR Spectroscopy Academic Press: San Diego (1996), which ishereby incorporated by reference in its entirety), extending the timedomain data to t_(2max)(¹⁵N)=36.0 ms (and yielding 64 points along ω₂after zero-filling prior to FT).

FIGS. 8(a)-(b) show plots of 2D [¹⁵N,¹H]-HSQC (Cavanagh et al., ProteinNMR Spectroscopy Academic Press: San Diego (1996), which is herebyincorporated by reference in its entirety) (FIG. 8(a)) and[ω₁(¹⁵N),ω₃(¹H^(N))] projection of ¹⁵N-resolved 3D spectra (FIG. 8(b))recorded for protein yqbG (95% H₂O/5% ²H₂O; 20 mM MES, pH=6.5, 100 mMNaCl, 10 mM DTT, 5 mM CaCl₂, 0.02% NaN₃). FIGS. 8(c) and 8(d) show[ω₂(¹⁵N;¹³C′),ω₃(¹H^(N))] planes from NCO-resolved experiments (κ=0.25)showing signals at Ω(¹⁵N)+κΩ(¹³C′) (left) and Ω(¹⁵N)+κΩ(¹³C′) (right).The green signal in FIGS. 8(a) and 8(b) arises from Tyr 12 and Asp 74having degenerate ¹⁵N and ¹H^(N) shifts; peaks are resolved in FIGS.8(c) and 8(d) due to non-degenerate ¹³C′ shifts and are shown as blueand red signals.

FIGS. 9(a)-(d) show contour plots of spectra recorded for 17 kDa proteinyqbG on Varian INOVA 600 spectrometer equipped with a cryogenic probe.FIG. 9(a) shows a plot of 2D [¹⁵N—¹H^(N)] HSQC; FIG. 9(b) shows a plotof basic spectra of (3,2)D HNNCO (Szyperski et al., J. Am. Chem. Soc.115:9307-9308 (1993); Brutscher et al., J. Magn. Reson. B109:238-242(1995), which are hereby incorporated by reference in their entirety)exhibiting peaks at ω₁:Ω(¹⁵N)±κΩ(¹³C′) (κ=0.25); FIG. 9(c) shows a plotof [ω₁(¹³C^(α);¹³C^(αβ)),ω₃(¹H^(N))]-strips taken from GFT L-(5,3)D HNNC^(αβ) C ^(α) (Atreya et al., Proc. Natl. Acad. Sci. USA 101:9642-9647(2004), which is hereby incorporated by reference in its entirety)(labeled as “a”) and L-(5,3)D HNN(CO)C ^(αβ) C ^(α) (labeled as “b”)showing a ¹⁵N-resolved “sequential walk”; and FIG. 9(d) shows a plot of[ω₁(¹³C^(α);¹³C^(αβ)),ω₃(¹H^(N))]-strips taken from G²FT L-(5,3)DHN{N,CO}C ^(αβ) C ^(α) (labeled as “a′”) and L-(5,3)D HN{NCO}{C ^(αβ) C^(α)} (labeled as “b′”) showing Ω(¹⁵N)±κΩ(¹³C′)-resolved sequentialwalks. Strips were taken at ω₂:Ω(¹⁵N) and ω₂:Ω(¹⁵N)±κΩ(¹³C′) (κ=0.25) ofresidues Ile (one-letter code: I) 122 to Lys (K) 125 (chemical shiftsindicated at bottom) and comprise peaks at ω₁:Ω(¹³C^(α))±Ω(¹³C^(α))(red) and ω₁:Ω(¹³C^(α))±Ω(¹³C^(αβ)) (blue). The acquisition parametersare given in Table 1. Peaks labeled “1”-“9” are assigned to: Gly (G) 121(3); Ile (I) 122 (1,2); Glu (E) 123 (4,5); Ala (A) 124 (6,7); Lys (K)125 (8,9). Sequential connectivities are indicated by dashed lines. InFIGS. 9(a) and 9(c), peaks belonging to Ala 50 are overlapped with thoseof Lys 125 due to ¹⁵N,¹H^(N) degeneracy (peaks are in green boxes).However, they are resolved in FIG. 9(b) due to their non-degenerate ¹³C′shifts and hence do not appear in strips taken at ω₂(¹⁵N; ¹³C′) of Lys125 shown in FIG. 9(d).

FIG. 10 shows the [ω₁(¹³C^(α);¹³C^(αβ)),ω₃(¹H^(N))]-strips taken fromG²FT (5,3)D HN{N,CO}{C ^(αα) C ^(α)} (“a”) and HN{NCO}{C ^(αβ) C ^(α)}(“b”) recorded for 17 kDa protein yqbG. Strips were taken atω₂(¹⁵N;¹³C′) of residues Ile 122 to Lys 125 (chemical shifts indicatedat bottom) and comprise peaks at Ω₀(¹³C^(α))±Ω₁(¹³C^(α)) (red) andΩ₀(¹³C^(α))±Ω₁(¹³C^(β)) (blue). Peaks “1”-“9” are assigned to Gly (oneletter code: G) 121 (3); Ile (I) 122 (1,2); Glu (E) 123 (4,5); Ala (A)124 (6,7); Lys (K) 125 (8,9). Connectivities are indicated by dashedlines: six sequential “walks” are established.

FIG. 11 depicts the r.f. pulse scheme of G²FT (5,3)D {C ^(αβ) C^(α)}{CON}HN. Rectangular 90° and 180° pulses are indicated by thin andthick vertical bars, respectively, and phases are indicated above thepulses. Where no r.f. phase is marked, the pulse is applied along x.High-power 90° pulse lengths are: 5.7 μs for ¹H, 15.0 μs for ¹³C and 40μs for ¹⁵N and κ=0.25. Pulses on ¹³C prior to t₁(¹³C) are applied athigh power, and ¹³C—¹H coupling during the first INEPT (Cavanagh et al.,Protein NMR Spectroscopy Academic Press: San Diego (1996), which ishereby incorporated by reference in its entirety) is achieved using a(90°_(x)-180°_(y)-90°_(x)) composite pulse. Subsequently, the 90° and180° pulse lengths applied on ¹³C^(αβ) (at a ¹H resonance frequency of600 MHz) are adjusted to 48 μs and 43 μs, respectively, during the firstt₁ delay [t₁(¹³C^(αβ))] and to 54 μs and 48 μs, respectively, during thesecond t₁ delay [t₁(¹³C^(α))] to minimize perturbation of ¹³C′ spins.All pulses applied on ¹³C′ are of SEDUCE (Cavanagh et al., Protein NMRSpectroscopy Academic Press: San Diego (1996), which is herebyincorporated by reference in its entirety) shape. Off-resonance 180°pulses with a length of 200 μs and 103 μs are used, respectively, todecouple ¹³C′ during t₁(¹³C^(αβ)), t₁(¹³C^(α)), and t₂(¹⁵N). Theduration of 90° pulse applied on-resonance at ¹³C′ is 200 μs. SEDUCE(Cavanagh et al., Protein NMR Spectroscopy Academic Press: San Diego(1996), which is hereby incorporated by reference in its entirety)off-resonance 180° pulses of duration 100 μs are used to decouple¹³C^(α) during t₂(¹³C′). WALTZ16 (Cavanagh et al., Protein NMRSpectroscopy Academic Press: San Diego (1996), which is herebyincorporated by reference in its entirety) is employed to decouple ¹H(r.f. field strength=6.0 kHz) during the heteronuclear magnetizationtransfers as well as to decouple ¹⁵N during acquisition (r.f.=1.7 kHz).The SEDUCE (Cavanagh et al., Protein NMR Spectroscopy, Academic Press:San Diego (1996), which is hereby incorporated by reference in itsentirety) sequence is used for decoupling ¹³C^(α) during t₂(¹⁵N). The ¹Hr.f. carrier position is placed at 4.78 ppm and that of ¹⁵N at 118.5ppm. The ¹³C carrier position is initially set to 43 ppm duringt₁(¹³C^(αβ)). This is then switched to 56 ppm during t₁(¹³C^(α))(indicated by an arrow as point a), to 175 ppm during t₂(¹³C′) (point b)and back to 56 ppm during t₂(¹⁵N) (at point c). The duration andstrengths of the pulsed rectangular z-field gradients (PFGs) are: G1 (1ms, 24 G/cm); G2 (0.5 ms, 8 G/cm); G3 (1.0 ms, 20 G/cm); G4 (0.5 ms, 8G/cm); G5 (1.25 ms, 30 G/cm); G6 (0.5 ms, 8 G/cm); G7 (0.125 ms, 29.5G/cm). The delays are: τ_(a)=1.7 ms, τ₁=350 μs, τ₂=2.8 ms, τ₃=2.65 ms,τ₄=7.2 ms, τ₅=4.4 ms, τ₆=24.6 ms, τ₇=24.6 ms, τ₈=5.5 ms, τ₉=4.6 ms,τ₁₀=1.0 ms. Phase cycling: φ₁=x; φ₂=x, x, −x,−x; φ₃=x, −x; φ₄=x;φ₆=x,−x; φ₇=x, x, −x, −x; φ₈=x; φ₉(receiver)=x, −x, −x, x. A sensitivityenhancement scheme (Kay et al., J. Am Chem. Soc. 114:10663-10665 (1992),which is hereby incorporated by reference in its entirety) is employed,i.e., the sign of G5 is inverted in concert with a 180° shift of φ₈Quadrature detection in t₁(¹³C^(α)) is accomplished by altering thephases φ₄ according to States-TPPI (Cavanagh et al., Protein NMRSpectroscopy Academic Press: San Diego (1996), which is herebyincorporated by reference in its entirety), whereas that of t₂(¹⁵N) isachieved by use of the sensitivity enhancement scheme. GFT NMRphase-cycle: φ₂=x, y; φ₅=2x, 2y, yielding, in conjunction withquadrature detection, 16 data sets which are linearly combined employinga G-matrix transformation with the G-matrix of Equation 10 (see DetailedDescription of the Invention section).

FIG. 12 shows the [ω₁(¹³C^(α); ¹³C^(αβ)),ω₃(¹H^(N))]-strips taken fromG²FT L-(5,3)D HN{N,CO}{C ^(αβ) C ^(α)} (labeled as “a”) and (5,3)D {C^(αβ) C ^(α)}{CON}HN (labeled as “b”) recorded for the 17 kDa proteinyqbG on Varian INOVA 600 spectrometer equipped with cryogenic probe.Strips were taken at ω₂:Ω(¹⁵N)±κΩ(¹³C′) (κ=0.25) of residues Ile(one-letter code: I) 122 to Lys (K) 125 (chemical shifts are indicatedat bottom) and comprise peaks at ω₁:Ω(¹³C^(α))±Ω(¹³C^(α)) (peaks labeled“1”, “3”, “4”, “6”, and “8”) and Ω₁:Ω(¹³C^(α))±Ω(¹³C^(β)) (peaks labeled“2”, “5”, “7”, and “9”). Acquisition parameters are given in Table 1.Peaks are assigned to the following residues: Gly (G) 121 (3); Ile (1)122 (1,2); Glu (E) 123 (4,5); Ala (A) 124 (6,7); Lys (K) 125 (8,9).Sequential connectivities are indicated by dashed lines, demonstratingthat six “sequential walks” are established [see also FIG. 10, where(5,3)D HN{NCO}{C ^(αβ) C ^(α)} instead of (5,3)D {C ^(αβ) C ^(α)}{CON}HNis used].

FIG. 13 depicts the r.f. pulse scheme of G²FT L-(5,3)D HN{NC ^(α)}{C^(αβ) C ^(α)}. Rectangular 90° and 180° pulses are indicated by thin andthick vertical bars, respectively, and phases are indicated above thepulses. Where no r.f. phase is marked, the pulse is applied along x.High-power 90° pulse lengths are: 5.7 μs for ¹H, 15.0 μs for ¹³C and 40μs for ¹⁵N, and κ=0.25. All 90° and 180° pulse lengths applied on¹³C^(αβ) are adjusted (at a ¹H resonance frequency of 750 MHz) to 39 μsand 34 μs, respectively, prior to and during the first t₁ delay[t₁(¹³C^(αβ))], and to 43 μs and 39 μs, respectively, during the secondt, delay [t₁(¹³C^(α))] in order to minimize perturbation of ¹³C′ spins.A 90° E-BURP2 pulse (Geen et al., J. Magn. Reson., 93:93-142 (1991),which is hereby incorporated by reference in its entirety) after the2^(nd) 90° ¹H pulse (1.2 ms; 0-6 ppm excitation; carrier: 3 ppm) enableswater flip-back (Cavanagh et al., Protein NMR Spectroscopy AcademicPress: San Diego (1996), which is hereby incorporated by reference inits entirety) and L-optimization (Atreya et al., Proc. Natl. Acad. Sci.USA 101:9642-9647 (2004); Pervushin et al., J. Am. Chem. Soc.124:12898-12902 (2002), which are hereby incorporated by reference intheir entirety). WALTZ16 (Cavanagh et al., Protein NMR Spectroscopy,Academic Press: San Diego (1996), which is hereby incorporated byreference in its entirety) is employed to decouple ¹⁵N (r.f.=1.70 kHz)during acquisition. The ¹H and ¹⁵N r.f. carriers are placed at theposition of the solvent line at 4.77 ppm, and at 118.5 ppm,respectively. The ¹³C carrier position is set to 43 ppm prior to andduring t₁(¹³C^(αβ)) and switched to 56 ppm during t₁(¹³C^(α)) (indicatedby the arrow). The duration and strengths of the pulsed rectangularz-field gradients (PFGs) are: G1 (1.0 ms, 20 G/cm); G2 (0.5 ms, 6 G/cm);G3 (1.0 ms, 20 G/cm); G4 (1.0 ms, 20 G/cm); G5 (1.25 ms, 30 G/cm); G6(0.5 ms, 4 G/cm); G7 (0.5 ms, 4 G/cm); G8 (0.125 ms, 29.5 G/cm). All PFGpulses are of rectangular shape. The delays are: τ₁=5.5 ms; τ₂=5.4 ms;τ₃=24 ms; τ₄=24 ms; τ₅=4.6 ms; τ₆=1.0 ms; τ_(a)=8.0 ms. Phase cycling:φ₁=x=x; φ₂=y,−y; φ₃=2(x),2(−x); =y; φ₄=x; φ₅=4(x), 4(−x); φ₆=x;φ₇(receiver)=x, −x, −x, x. A sensitivity enhancement scheme (Kay et al.,J. Am. Chem. Soc. 114:10663-10665 (1992), which is hereby incorporatedby reference in its entirety) is employed, i.e., the sign of G5 isinverted in concert with a 180° shift of 45. Quadrature detection int₁(¹³C^(α)) is accomplished by altering the phases φ₃ according toStates-TPPI, whereas quadrature detection in t₂(¹⁵N) is achieved by useof the sensitivity enhancement scheme. GFT NMR phase-cycle: φ₁=2(x, y);φ₂=y, x, x, y, yielding, in conjunction with quadrature detection, 16data sets which are linearly combined employing a G-matrixtransformation with the G-matrix of Equation 10 (see DetailedDescription of the Invention section).

FIG. 14 depicts the r.f. pulse scheme of G²FT L-(5,3)D HN{N(CO)C ^(α)}{C^(αβ) C ^(α)}. Rectangular 90° and 180° pulses are indicated by thin andthick vertical bars, respectively, and phases are indicated above thepulses. Where no r.f. phase is marked, the pulse is applied along x.High-power 90° pulse lengths are: 5.7 μs for ¹H, 15.0 μs for ¹³C and 40μs for ¹⁵N, and κ=0.25. 90° and 180° pulse lengths applied on ¹³C^(αβ)are adjusted (at a ¹H resonance frequency of 750 MHz) to 39 μs and 34μs, respectively, prior to and during the first t₁ delay [t₁(¹³C^(α))]and to 43 μs and 39 μs, respectively, during the second t₁ delay[t₁(¹³C^(α))] to minimize perturbation of ¹³C′ spins. A 90° E-BURP2pulse (Geen et al., J. Magn. Reson., 93:93-142 (1991), which is herebyincorporated by reference in its entirety) after the 2^(nd) 90° ¹H pulse(1.2 ms; 0-6 ppm excitation; carrier: 3 ppm) enables water flip-back(Cavanagh et al., Protein NMR Spectroscopy Academic Press: San Diego(1996), which is hereby incorporated by reference in its entirety) andL-optimization (Atreya et al., Proc. Natl. Acad. Sci. USA 101:9642-9647(2004); Pervushin et al., J. Am. Chem. Soc. 124:12898-12902 (2002),which are hereby incorporated by reference in their entirety). SEDUCE(Cavanagh et al., Protein NMR Spectroscopy Academic Press: San Diego(1996), which is hereby incorporated by reference in its entirety)off-resonance 180° pulses of duration 200 μs and 103 μs, respectively,are used to decouple ¹³C′ during t₁(¹³C^(αβ)) and t₁(¹³C^(α)). The 90°and 180° pulse lengths for the sinc lobe pulse on-resonance at ¹³C′ is88 μs and 81 μs, respectively. A six-pulse composite sequence is used tosimultaneously invert/refocus ¹³C^(α)/¹³C′ magnetization during¹³C^(α)—¹³C′ polarization transfers. (In the three sets of subspectraconstituting (5,3)D HN{N,CO}{C ^(αβ) C ^(α)}, (5,3)D HN{NCO}{C ^(αβ) C^(α)} and (4,3)D HNNC ^(αβ) C ^(α), nine sequential walks areestablished (FIG. 9). Hence, combination of all three pairs of (5,3)DG²FT experiments described in the present application can provide atotal of 24 independent sequential walks.) The SEDUCE (Cavanagh et al.,Protein NMR Spectroscopy Academic Press: San Diego (1996), which ishereby incorporated by reference in its entirety) sequence is used fordecoupling of ¹³C^(α) during t₂(¹⁵N). WALTZ16 (Cavanagh et al., ProteinNMR Spectroscopy Academic Press: San Diego (1996), which is herebyincorporated by reference in its entirety) is employed to decouple of¹⁵N (r.f.=1.70 kHz) during acquisition. The ¹H r.f. carrier is placed atthe position of the solvent line at 4.77 ppm after the first selectivepulse on ¹H. The ¹⁵N carrier position is set to 118.5 ppm. The ¹³Ccarrier position is set initially to 175 ppm, then switched to 43 ppmprior to t₁(¹³C^(αβ)) (indicated by an arrow as point a), to 56 ppmduring t₁(¹³C^(α)) (at b) and back to 175 ppm (at c) during the reverse¹³C —¹³C^(α) polarization transfer. The duration and strengths of thepulsed rectangular z-field gradients (PFGs) are: G1 (1.0 ms, 24 G/cm);G2 (0.5 ms, 8 G/cm); G3 (1.0 ms, 20 G/cm); G4 (0.5 ms, 4 G/cm); G5 (1.0ms, 20 G/cm); G6 (0.5 ms, 8 G/cm); G7 (1.25 ms, 30 G/cm); G8 (0.5 ms, 4G/cm); G9 (0.125 ms, 29.5 G/cm). The delays are: τ₁=5.4 ms, τ₂=5.4 ms,τ₃=24 ms, τ₄=24 ms, τ₅=4.6 ms, τ₆=1.0 ms, τ_(a)=8.0 ms, τ_(b)=7.0 ms.Phase cycling: φ₁=x, −x; φ₂=y; φ₃=2(x),2(−x); φ₄=x, φ₅=4(x), 4(−x);φ₆=x; φ₇(receiver)=x, −x, −x, x. A sensitivity enhancement scheme (Kayet al., J. Am. Chem. Soc. 114:10663-10665 (1992), which is herebyincorporated by reference in its entirety) is employed, i.e., the signof G7 is inverted in concert with a 180° shift of φ₆. Quadraturedetection in t₁(¹³C^(α)) is accomplished by altering the phases φ₃according to States-TPPI, whereas quadrature detection in t₂(¹⁵N) isachieved by use of the sensitivity enhancement scheme. GFT NMRphase-cycle: φ₁=2(x, y); φ₂=y, x, x, y, yielding, in conjunction withquadrature detection, 16 data sets which are linearly combined employinga G-matrix transformation with the G-matrix of Equation 10 (see DetailedDescription of the Invention section).

FIG. 15 shows the [ω₁(¹³C^(α);¹³C^(αβ)),ω₃(¹H^(N))]-strips taken fromG²FT L-(5,3)D HN{NC ^(α)}{C ^(α) C ^(αβ)}(labeled as “a”) and L-(5,3)DHN{N(CO)C ^(α)}{C ^(α) C ^(αβ)}(labeled as “b”) recorded for the 13.5kDa protein rsp24e equipped with a ¹H{¹³C,¹H} triple resonance probe.Strips were taken at ω₂:Ω(¹⁵N)+κΩ(¹³C′) (left) and ω₂:Ω(¹⁵N)−κΩ(¹³C′)(right) (κ=0.25) of residues Leu (one-letter code: L) 47 to Leu (L) 50(chemical shifts are indicated at bottom) and comprise peaks atω₁:Ω(¹³C^(α))±Ω(¹³C^(α)) (peaks “1”, “3”, “4”, “7”) andΩ(¹³C^(α))±(¹³C^(β)) (peaks “2”, “4”, “6”, “8”). The acquisitionparameters are given in Table 1. The peaks are assigned to the followingresidues: Leu (L) 47 (“1”, “2”), Glu (E) 48 (“3”, “4”); Leu (L) 49 (“5”,“6”); Leu (L) 50 (“7”, “8”). Sequential connectivities are indicated bydashed lines, demonstrating that six “sequential walks” are established.

FIG. 16 shows composite plots of [ω₁(¹³C^(α); ¹³C^(αβ)), ω₃(¹H^(N))]strips taken from the basic spectra of G²FT (5,3)D HN{NC ^(α)}{C ^(αβ) C^(α)}. The four basic spectra are grouped into two sets, B1 and B2,comprising peaks at Ω₀(¹⁵N_(i))+Ω₁(¹³C^(α) _(i)) andΩ₀(¹⁵N_(i))−Ω₁(¹³C^(α) _(i)) along ω₂, respectively. B1 and B2 eachcontain two spectra (labeled as “b1” and “b2”) comprising peaks atΩ₀(¹³C^(α) _(i/i-1))±Ω₁(¹³C^(α/β) _(i/i-1)) along ω₁. Positive andnegative peaks are shown, respectively, with solid and dotted contourlines. As an example, strips are shown for the residue Ala 55 of the 7kDa protein Z-domain. Peaks labeled 1-4 in “b1” and “b2” correspond tothe following linear combination of chemical shifts along ω₁:

-   -   1. Ω₀(¹³C^(α) _(i-1))+Ω₁(¹³C^(α) _(i-1))    -   2. Ω₀(¹³C^(α) _(i-1))+Ω₁(¹³C^(β) _(i-1))    -   3. Ω₀(¹³C^(α) _(i-1))−Ω₁(13C^(β) _(i-1))    -   4. Ω₀(¹³C^(α) _(i-1))−Ω₁(13C^(α) _(i-1))

FIG. 17 shows composite plots of [ω₁(¹³C^(α); ¹³C^(αβ)), ω₃(¹H^(N))]strips taken from the basic spectra of G²FT (5,3)D HN{N(CO)C ^(α)}{C^(αβ) C ^(α)}. The four basic spectra are grouped into two sets, B1 andB2, comprising peaks at Ω₀(¹⁵N_(i))+Ω₁(¹³C^(α) _(i-1)) andΩ₀(¹⁵N_(i))−Ω₁(¹³C^(α) _(i-1)) along ω₂, respectively. B1 and B2 eachcontain two spectra (labeled as “b1” and “b2”) comprising peaks atΩ₀(¹³C^(α) _(i-1))±Ω₁(¹³C^(α/β) _(i-1)) along ω₁. Positive and negativepeaks are shown, respectively, with solid and dotted contour lines. Asan example, strips are shown for the residue Lys 63 of the 7 kDa proteinZ-domain. Peaks labeled 1-4 in “b1” and “b2” correspond to the followinglinear combination of chemical shifts along ω₁:

-   -   1. Ω₀(¹³C^(α) _(i-1))+Ω₁(¹³C′^(α) _(i-1))    -   2. Ω₀(¹³C^(α) _(i-1))+Ω₁(¹³C^(β) _(i-1))    -   3. Ω₀(¹³C^(α) _(i-1))−Ω₁(¹³C^(β) _(i-1))    -   4. Ω₀(¹³C^(α) _(i-1))−Ω₁(¹³C^(α) _(i-1))

FIG. 18 depicts the r.f pulse scheme of G²FT (5,3)D HN{N,CO}{C ^(α) H^(α)}. Rectangular 90° and 180° pulses are indicated by thin and thickvertical bars, respectively, and phases are indicated above the pulses.Where no r.f. phase is marked, the pulse is applied along x. High-power90° pulse lengths are: 5.7 μs for ¹H, 15.0 μs for ¹³C and 40 μs for ¹⁵Nand κ=0.25. A six-pulse composite sequence (Shaka, Chem. Phy. Lett.,120:201-205 (1985), which is hereby incorporated by reference in itsentirety) is used to simultaneously transfer magnetization from ¹⁵N(i)to ¹³C^(α) (i/i−1) and ¹³C (i−1), and back. The lengths of the 90° and180° pulses applied on ¹³C^(α) are adjusted (at a ¹H resonance frequencyof 600 MHz) to 51.6 μs and 46 μs, respectively, during t₁(¹³C^(α)) tominimize perturbation of ¹³C′ spins. The width of the 90° pulses appliedto ¹³CO pulse is 52 μs and the corresponding off-resonance 180° pulse isapplied with same power. A rectangular phase modulated off-resonance180° pulse with a length of 46 μs is used to decouple ¹³C^(α) duringt₂(¹³C ). WALTZ16 (Cavanagh et al., Protein NMR Spectroscopy AcademicPress: San Diego (1996), which is hereby incorporated by reference inits entirety) (r.f. field strength=6.0 kHz) is employed to decouple ¹Hduring the heteronuclear magnetization transfers as well as to decouple¹⁵N during acquisition (r.f.=1.7 kHz). The scaling factor κ′ for ¹Hchemical shift evolution during t₁ is set to 1.0. The ¹H and ¹⁵N r.f.carriers are set to 4.78 ppm and 118.5 ppm, respectively. The ¹³Ccarrier position is initially set to 56 ppm, and switched to 175 ppmbefore the first 90° pulse on ¹³C′, and back to 56 ppm after the second90° pulse on ¹³C′. ¹³C^(α)-frequency labeling is achieved in a semiconstant-time fashion with (at 600 MHz): t₁ ^(a)(0)=1.7 ms, t₁ ^(b)(0)=1μs, t₁ ^(c)(0)=1.701 ms, Δt₁ ^(a)=12.5 μs, Δt₁ ^(b)=6.6 μs, Δt₁^(c)=−5.9 μs. Hence, the fractional increase of the semi constant-timeperiod with t₁ equals to λ=1+Δt₁ ^(c)/Δt₁ ^(a)=0.53. The duration andstrengths of the pulsed rectangular z-field gradients (PFGs) are: G1 (1ms, 20 G/cm); G2 (0.5 ms, 8 G/cm); G3 (1.0 ms, 20 G/cm); G4 (0.5 ms, 16G/cm); G5 (1.25 ms, 30 G/cm); G6 (0.5 ms, 8 G/cm); G7 (0.125 ms, 29.5G/cm). The delays are: τ₁=5.4 ms, τ₂=5.6 ms, τ₃=28 ms, τ₄=1.7 ms, τ₅=1.0ms, τ_(a)=1.7 ms. Phase cycling: φ₁=x, −x; φ₂=x, x, −x,−x; φ₃=x; φ₄=y;φ₅=4(x)4(−x); φ₆=x; φ₇(receiver)=x, −x, −x, x. A sensitivity enhancementscheme (Kay et al., J. Am. Chem. Soc. 114:10663-10665 (1992), which ishereby incorporated by reference in its entirety) is employed, i.e., thesign of G₅ is inverted in concert with a 180° shift of φ₆. Quadraturedetection in t₁(¹³C^(α)) is accomplished by altering the phases φ₄according to States-TPPI, whereas quadrature detection in t₂(¹⁵N) isachieved by use of the sensitivity enhancement scheme. GFT NMRphase-cycle: φ₁=x, y; φ₃=2x, 2y, yielding in conjunction with quadraturedetection 16 data sets which are linearly combined employing a G-matrixtransformation with the G-matrix of Equation 10 (see DetailedDescription of the Invention section).

FIG. 19 depicts the r.f. pulse scheme of G²FT (5,3)D {H ^(α) C^(α)}{CON}HN. Rectangular 90° and 180° pulses are indicated by thin andthick vertical bars, respectively, and phases are indicated above thepulses. Where no r.f. phase is marked, the pulse is applied along x. Thehigh power 90° pulse lengths were: 5.8 μs for ¹H and 15.0 μs for ³¹C,and 38 μs for ¹⁵N, and κ=0.25. Pulses on ¹³C prior to t₁(¹³C) areapplied at high power, and ¹³C decoupling during t₁(¹H) is achievedusing a (90°_(x)-180°_(y)-90°_(x)) composite pulse. Subsequently, the90° and 180° pulse lengths of ¹³C^(α) are adjusted (at a ¹H resonancefrequency of 600 MHz) to 54 μs and 46 μs, respectively, to minimizeperturbation of the ¹³C′ spins. A six-pulse composite sequence (Shaka,Chem. Phy. Lett., 120:201-205 (1985), which is hereby incorporated byreference in its entirety) is used to simultaneously invert/refocus¹³C^(α)/¹³C′ magnetization during ¹³C^(α)—¹³C′ polarization transfer.The length of 90° pulses applied to ¹³C′ is 52 μs and the corresponding180° pulses are applied with same power. WALTZ16 (Cavanagh et al.,Protein NMR Spectroscopy Academic Press: San Diego (1996), which ishereby incorporated by reference in its entirety) is employed todecouple ¹H (r.f. field strength=6.0 kHz) during the heteronuclearmagnetization transfers as well as to decouple ¹⁵N during acquisition(r.f.=1.7 kHz). The SEDUCE (Cavanagh et al., Protein NMR SpectroscopyAcademic Press: San Diego (1996), which is hereby incorporated byreference in its entirety) sequence is used for decoupling of ¹³C^(α)during the ¹⁵N chemical shift evolution period. The ¹H r.f. carrier isplaced at the position of the solvent line at 4.78 ppm. The ¹³C^(α)carrier is set to 56 ppm except during t₂(¹³C′), where it is set to 175ppm. The ¹⁵N r.f. carrier is set to 120.9 ppm. The duration andstrengths of the pulsed rectangular z-field gradients (PFGs) are: G1 (1ms, 24 G/cm); G2 (0.1 ms, 8 G/cm); G3 (1 ms, 20 G/cm); G4 (0.5 ms, 8G/cm); G5 (1.0 ms, 20 G/cm); G6 (1.0 ms, 20 G/cm); G7 (1.25 ms, 30G/cm); G8 (0.5 ms, 8 G/cm); G9 (0.125 ms, 29.5 G/cm). The delays are:τ₁=850 μs, τ₂=3.6 ms, τ₃=4.4 ms, τ₄=12.5 ms, τ₅=8 ms, τ₆=4.5 ms, τ₇=24ms, τ₈=5.5 ms, τ₉=4.6 ms, τ₁₀=1 ms. ¹H-frequency labeling is achieved ina semi constant-time fashion with t₁ ^(a)(0)=1.7 ms, t₁ ^(b)(0)=1 μs, t₁^(c)(0)=1.701 ms, Δt₁ ^(a)=60 μs, Δt₁ ^(b)=35.4 μs, Δt₁ ^(c)=−24.6 μs.Hence, the fractional increase of the semi constant-time period with t₁equals to λ=1+Δt₁ ^(c)/Δt₁ ^(a)=0.58. Phase cycling: φ₁=x; φ₂=x, −x;φ₃=x; φ₄=4(x), 4(−x); φ₅=x; φ₆(receiver)=x, −x, −x, x. A sensitivityenhancement scheme (Kay et al., J. Am. Chem. Soc. 114:10663-10665(1992), which is hereby incorporated by reference in its entirety) isemployed, i.e., the sign of G7 is inverted in concert with a 180° shiftof φ₅. Quadrature detection in t₁(¹³C^(α)) is accomplished by alteringthe phases φ₂ according to States-TPPI, quadrature detection in t₂(¹⁵N)is achieved by use of the sensitivity enhancement scheme. GFT NMRphase-cycle: φ₁=x, y; φ₃=2x, 2y, yielding, in conjunction withquadrature detection, 16 data sets which are linearly combined employinga G-matrix transformation with the G-matrix of Equation 10 (see DetailedDescription of the Invention section).

FIG. 20 shows the [ω₁(¹³C^(α);¹H^(α)),ω₃(¹H^(N))]-strips taken from G²FT(5,3)D HN{N,CO}{C^(α)H^(α)}(labeled as “a”) and (5,3)D {H ^(α) C^(α)}{CON}HN (labeled as “b”) recorded for the 8 kDa protein Z-domain(Montelione et al., Nature Struct. Biol. 7:982-984 (2002), which ishereby incorporated by reference in its entirety) on Varian INOVA 600spectrometer equipped with a cryogenic probe. Strips were taken atω₂:Ω(¹⁵N)±κΩ(¹³C′) (κ=0.25) of residues Leu (one-letter code: L) 58 toGlu (E) 60 (chemical shifts are indicated at bottom) and comprise peaksat ω₁:Ω(¹³C^(α))±Ω(¹H^(α)) (peaks labeled “1”-“4”). These peaks havebeen assigned to the following residues: Leu (L) 57 (“1”), Leu (L) 58(“2”); Ala (A) 59 (“3”); Glu (E) 60 (“4”). Sequential connectivities areindicated by dashed lines, demonstrating that four sequential walks areestablished.

FIG. 21 shows composite plots of [ω₁(¹³C^(α); ¹H^(α)), ω₃(¹H^(N))]strips taken from the basic and central peak spectra of G²FT (5,3)DHN{N,CO}{C ^(α) H ^(α)}. The four basic spectra are grouped into twosets, B1 and B2, comprising peaks at Ω₀(¹⁵N_(i))+Ω₁(¹³C′_(i-1)) andΩ₀(¹⁵N_(i))−Ω₁(¹³C′_(i-1)) along ω₂, respectively. B1 and B2 eachcontain two spectra (labeled as “b1” and “b2”) comprising peaks atΩ₀(¹³C^(α) _(i/i-1))±Ω₁(¹H^(α) _(i/i-1)) along ω₁. The first ordercentral peak spectrum (labeled as “b3”) comprising peaks at Ω₀(¹³C^(α)_(i/i-1)) along ω₁ is obtained by separately recording a G²FT (4,3)DHN{N,CO}C ^(α). As an example, strips are shown for the residue Ala 55of Z-domain. Peaks labeled 1-6 in “b1”, “b2”, and “b3” correspond to thefollowing linear combination of chemical shifts along ω₁:

-   -   1. Ω₀(¹³C^(α) _(i))+Ω₂(¹H^(α) _(i))    -   2. Ω₀(¹³C^(α) _(i-1))+Ω₂(¹H^(α) _(i-1))    -   3. Ω₀(¹³C^(α) _(i))−Ω₂(¹H^(α) _(i))    -   4. Ω₀(¹³C^(α) _(i-1))−Ω₂(¹H^(α) _(i-1))    -   5. Ω₀(¹³C^(α)i)    -   6. Ω₀(¹³C^(α) _(i-1))

FIG. 22 depicts the r.f pulse scheme of G²FT (4,3)D HN{N,CO}C^(α).Rectangular 90° and 180° pulses are indicated by thin and thick verticalbars, respectively, and phases are indicated above the pulses. Where nor.f. phase is marked, the pulse is applied along x. High-power 90° pulselengths are: 5.7 μs for ¹H, 15.0 μs for ¹³C and 40 μs for ¹⁵N. Asix-pulse composite sequence (Shaka, Chem. Phy. Lett., 120:201-205(1985), which is hereby incorporated by reference in its entirety) isused to tranfer magnetization from ¹⁵N(i) to ¹³C^(α) (i/i−1) and ¹³C(i−1) simultaneously and back. The 90° and 180° pulse lengths applied on¹³C^(α) (at a ¹H resonance frequency of 600 MHz) are adjusted to to 51.6μs and 46 μs, respectively, during the t₁ delay period (t₁(¹³C^(α))) tominimize perturbation of ¹³C′ spins. The width of the 90° pulses appliedto ¹³CO pulse is 52 μs and the corresponding off-resonance 180° pulse isapplied with same power. A hard off-resonance 180° pulse with a lengthof 46 μs is used to decouple ¹³C^(α) during during t₂(¹³C ). WALTZ16 isemployed to decouple ¹⁵N during acquisition (r.f.=1.78 kHz). The ¹H r.f.carrier position is placed at 4.78 ppm and that of ¹⁵N at 118.5 ppm. The¹³C carrier position is initially set to 56 ppm. This is then switchedto 175 ppm before the first 90° pulse on ¹³C′ and back to 56 ppm afterthe second 90° pulse on ¹³C′. The duration and strengths of the pulsedz-field gradients (PFGs) are: G1 (1 ms, 20 G/cm); G2 (500 μs, 8 G/cm);G3 (1.0 ms, 20 G/cm); G4 (500 μs, 16 G/cm); G5 (1.25 ms, 30 G/cm); G6(500 μs, 8 G/cm); G7 (125 μs, 29.5 G/cm). All PFG pulses are ofrectangular shape. The delays are: τ₁=5.4 ms, τ₂=5.6 ms, τ₃=28 ms,τ₄=1.7 ms, τ₅=1.0 ms, τ_(a)=1.7 ms. Phase cycling: φ₁=x, −x; φ₂=x, x,−x,−x; φ₃=x; φ₄=y; φ₅=4(x)4(−x); φ₆=x; φ₇(receiver)=x, −x, −x, x. Asensitivity enhancement scheme (Kay et al., J. Am. Chem. Soc.114:10663-10665 (1992), which is hereby incorporated by reference in itsentirety) is employed, i.e., the sign of G₅ is inverted in concert witha 180° shift of φ₆. Quadrature detection in t₁(¹³C^(α)) is accomplishedby altering the phases φ₂ according to States-TPPI whereas that oft₂(¹⁵N) is achieved via gradient selection of coherences using G5.GFT-NMR super phase-cycle for recording the 2 basic spectra along ω₂ is:φ₁=x,y.

FIG. 23 shows composite plots of [ω₁(¹³C^(α); ¹H^(α)), ω₃(¹H^(N))]strips taken from the basic and central peak spectra of G²FT (5,3)D {H^(α) C ^(α)}{CON} HN. The four basic spectra are grouped into two sets,B1 and B2, comprising peaks at Ω₀(¹⁵N_(i))+Ω₁(¹³C′_(i-1)) andΩ₀(¹⁵N_(i))−Ω₁(¹³C′_(i-1)) along ω₂, respectively. B1 and B2 eachcontain two spectra (labeled as “b1” and “b2”) comprising peaks atΩ₀(¹³C^(α) _(i-1))±Ω₁(¹H^(α) _(i-1)) along ω₁. The first order centralpeak spectrum (labeled as “b3”) comprising peaks at Ω₀(¹³C^(α) _(i-1))along ω₁ is obtained by omitting the frequency labeling of H^(α). As anexample, strips are shown for the residue His 31 of Z-domain. Peakslabeled 1-3 in “b1”, “b2”, and “b3” correspond to the following linearcombination of chemical shifts along ω₁:

-   -   1. Ω₀(¹³C^(α) _(i-1))+Ω₁(¹H^(α) _(i-1))    -   2. Ω₀(¹³C^(α) _(i-1))−Ω₁(¹H^(α) _(i-1))    -   3. Ω₀(¹³C^(α) _(i-1))

FIG. 24 depicts the r.f. pulse scheme of G²FT (6,3)D {H ^(αβ) C^(α)}{CON}HN. Rectangular 90° and 180° pulses are indicated by thin andthick vertical bars, respectively, and phases are indicated above thepulses. Where no r.f. phase is marked, the pulse is applied along x.High-power 90° pulse lengths are: 5.7 μs for ¹H, 15.0 μs for ¹³C and 40μs for ¹⁵N and κ=0.25. Pulses on ¹³C prior to t₁(¹³C) are applied athigh power, and ¹³C decoupling during t₁(¹H) is achieved using a(90°_(x)-180°_(y)-90°_(x)) composite pulse. Subsequently, the lengths of90° and 180° pulses applied on ¹³C^(αβ) are adjusted (at a ¹H resonancefrequency of 750 MHz) to 39 μs and 34 μs, respectively, duringt₁(¹³C^(αβ)), and to 43 μs and 39 μs, respectively, during t₁(¹³C^(α))in order to minimize perturbation of ¹³C′ spins. All pulses applied on¹³C′ are of SEDUCE (Cavanagh et al., Protein NMR Spectroscopy AcademicPress: San Diego (1996), which is hereby incorporated by reference inits entirety) shape. Off-resonance 180° pulses with a length of 200 μsand 103 μs is used, respectively, to decouple ¹³C′ during t₁(¹³C^(αβ)),t₁(¹³C^(α)) and t₂(¹⁵N). The duration of 90° pulses applied on-resonanceon ¹³C′ is 200 μs. WALTZ16 (Cavanagh et al., Protein NMR SpectroscopyAcademic Press: San Diego (1996), which is hereby incorporated byreference in its entirety) is employed to decouple ¹H during theheteronuclear magnetization transfer and ¹⁵N during acquisition(r.f.=1.78 kHz). The ¹H and ¹⁵N r.f. carrier positions are placed at4.78 ppm and 118.5 ppm, respectively. The ¹³C carrier position isinitially set to 43 ppm during t₁(¹³C^(αβ)), and switched to 56 ppmduring t₁(¹³C^(α)) (indicated by an arrow as point a), to 175 ppm duringt₂(¹³C′) (at b) and back to 56 ppm during t₂(¹⁵N) (at c). ¹H-frequencylabeling (at a ¹H resonance frequency of 750 MHz) is achieved in a semiconstant-time fashion with t₁ ^(a)(0)=1.7 ms, t₁ ^(b)(0)=1 μs, t₁^(c)(0)=1.701 ms, Δt₁ ^(a)=33.3 μs, Δt₁ ^(b)=17.0 μs, Δt₁ ^(c)=−16 μs.Hence, the fractional increase of the semi constant-time period with t₁equals to λ=1+Δt₁ ^(c)/Δt₁ ^(a)=0.51. The duration and strengths of thepulsed rectangular z-field gradients (PFGs) are: G1 (1 ms, 24 G/cm); G2(0.5 ms, 8 G/cm); G3 (0.5 ms, 8 G/cm); G4 (1.0 ms, 20 G/cm); G5 (1.25ms, 30 G/cm); G6 (0.5 ms, 8 G/cm); G7 (0.125 ms, 29.5 G/cm). The delaysare: τ₁=350 μs, τ₂=2.8 ms, τ₃=3.15 ms, τ₄=7.2 ms, τ₅=4.4 ms, τ₆=24.6 ms,τ₇=24.6 ms, τ₈=5.5 ms, τ₉=4.6 ms, τ₁₀=1.0 ms. Phase cycling: φ₁=x; φ₂=x,x, −x,−x; φ₃=x, −x; φ₄=x; φ₆=x, −x; φ₇=x, x, −x, −x; φ₈=x;φ₉(receiver)=x, −x, −x, x. A sensitivity enhancement scheme (Kay et al.,J. Am Chem. Soc. 114:10663-10665 (1992), which is hereby incorporated byreference in its entirety) is employed, i.e., the sign of G₆ is invertedin concert with a 180° shift of φ₈. Quadrature detection in t₁(¹³C^(α))is accomplished by altering the phases φ₄ according to States-TPPI,whereas quadrature detection of t₂(¹⁵N) is achieved by used of thesensitivity enhancement scheme. GFT NMR phase-cycle: φ₁=x, y; φ₂=2x, 2y;φ₅=4(x), 4(y), yielding, in conjunction with quadrature detection, 32data sets which are linearly combined employing a G-matrixtransformation with the G-matrix of Equation 11 (see DetailedDescription of the Invention section). For acquisition of central peaksalong ω₁ which are derived from ¹³C steady state magnetization, a seconddata set with φ₁=−x is collected. The sum and the difference of the tworesulting data sets generate two subspectra containing the central peaksand peak pairs.

FIG. 25 illustrates peak patterns observed in G²FT (6,3)D {H ^(αβ) C^(αβ) C ^(α)}{CON}HN recorded for the 8.6 kDa protein ubiquitin onVarian INOVA 750 spectrometer equipped with a ¹H{¹³C,¹H} tripleresonance probe. [ω₁(¹³C^(α);C^(αβ);¹H^(αβ)),ω₃(¹H^(N))] and[ω₁(¹³C^(α);C^(αβ)),ω₃(¹H^(N))]-strips were taken, respectively, fromthe basic spectra (labeled “b1”-“b4”) comprising peaks at ω₁:Ω(¹³C^(α)_(i-1))±ω(¹³C^(α/β) _(i-1))±Ω(¹H^(α/β) _(i-1)) and first order centralpeak spectra (labeled “b5” and “b6”) comprising peaks at ω₁:Ω(¹³C^(α)_(i-1))±Ω(¹³C^(α/β) _(i-1)) at ω₂:Ω(¹⁵N)+κΩ(¹³C′) (right) andω₂:Ω(¹⁵N)−κΩ(¹³C′) (left) (κ=0.5) of residue Ala 46 (chemical shiftsindicated at bottom). Acquisition parameters are given in Table 1. Peakslabeled 1-16 in “b1”-“b6” correspond to the following linear combinationof chemical shifts of Phe 45 along ω₁:Ω₀(¹³C^(α))±Ω₁(¹³C^(α))±Ω₂(¹H^(α)) (“1”, “4”, “9”, “12”);Ω₀(¹³C^(α))±Ω₁(¹³C^(β))±Ω₂(¹H^(β2)) (“2”, “5”, “8”, “11”);Ω₀(¹³C^(α))±Ω₁(¹³C^(β))±Ω₂(¹H^(β3)) (“3”, “6”, “7”, “10”);Ω₀(¹³C^(α))±Ω₁(¹³C^(α)) (“13”, “16”) and Ω₀(¹³C^(α))±Ω₁(¹³C^(β)) (“14”,“15”). The subspectra “b1”-“b6” encode the following linear combinationof shifts:

-   -   b1: Ω₀(¹³C^(α))+Ω₁(¹³C^(α))+Ω₂(¹H^(α));        Ω₀(¹³C^(α))+Ω₁(¹³C^(β))+Ω₂(¹H^(β2/β3));    -   b2: Ω₀(¹³C^(α))+Ω₁(¹³C^(α))−Ω₂(¹H^(α));        Ω₀(¹³C^(α))+Ω₁(¹³C^(β))−Ω₂(¹H^(β2/β3));    -   b3: Ω₀(¹³C^(α))−Ω₁(¹³C^(α))+Ω₂(¹H^(α));        Ω₀(¹³C^(α))−Ω₁(¹³C^(β))+Ω₂(¹H^(β2/β3));    -   b4: Ω₀(¹³C^(α))−Ω₁(¹³C^(α))−Ω₂(¹H^(α));        Ω₀(¹³C^(α))−Ω₂(¹³C^(β))−Ω₂(¹H^(β2/β3));    -   b5: Ω₀(¹³C^(α))+Ω₁(¹³C^(α)); Ω₀(¹³C^(α))−Ω₁(¹³C^(β));    -   b6: Ω₀(¹³C^(α))−Ω₁(¹³C^(α)); Ω₀(¹³C^(α))−Ω₁(¹³C^(β)).

FIG. 26 shows composite plots of [φ₁(¹³C; ¹³C, ¹H), ω₃(¹H)] strips takenfrom the basic spectra (labeled b1-b4) and first order central peakspectra (labeled b5 and b6) of (5,3)D HC(C)C—CH. As an example, stripscorresponding to ω₂(¹³C^(δ)) and ω₃(¹H^(δ)) chemical shifts for residueArg 88 of the 14 kDa protein PfR13 are shown. Peaks labeled 1-22correspond to the following linear combination of chemical shifts alongω₁: Corresponding peak type in 4D Relay-HC(C)CH (peaks 1-16) and 3DRelay (H)C(C)CH (peaks 17-22)  1. Ω₀(¹³C^(δ)) + Ω₁(¹³C^(δ)) +Ω₂(¹H^(δ2/δ3)) “Diagonal peak”  2. Ω₀(¹³C^(δ)) + Ω₁(¹³C^(γ)) +Ω₂(¹H^(γ2)) “Cross peak”  3. Ω₀(¹³C^(δ)) + Ω₁(¹³C^(γ)) + Ω₂(¹H^(γ3))“Cross peak”  4. Ω₀(¹³C^(δ)) + Ω₁(¹³C^(β)) + Ω₂(¹H^(β2/β3)) “Relay peak” 5. Ω₀(¹³C^(δ)) + Ω₁(¹³C^(δ)) − Ω₂(¹H^(δ2/δ3)) “Diagonal peak”  6.Ω₀(¹³C^(δ)) + Ω₁(¹³C^(γ)) − Ω₂(¹H^(γ2)) “Cross peak”  7. Ω₀(¹³C^(δ)) +Ω₁(¹³C^(γ)) − Ω₂(¹H^(γ3)) “Cross peak”  8. Ω₀(¹³C^(δ)) + Ω₁(¹³C^(β)) −Ω₂(¹H^(β2/β3)) “Relay peak”  9. Ω₀(¹³C^(δ)) − Ω₁(¹³C^(δ)) +Ω₂(¹H^(δ2/δ3)) “Diagonal peak” 10. Ω₀(¹³C^(δ)) − Ω₁(¹³C^(γ)) +Ω₂(¹H^(γ2)) “Cross peak” 11. Ω₀(¹³C^(δ)) − Ω₁(¹³C^(γ)) + Ω₂(¹H^(γ3))“Cross peak” 12. Ω₀(¹³C^(δ)) − Ω₁(¹³C^(β)) + Ω₂(¹H^(β2/β3)) “Relay peak”13. Ω₀(¹³C^(δ)) − Ω₁(¹³C^(δ)) − Ω₂(¹H^(δ2/δ3)) “Diagonal peak” 14.Ω₀(¹³C^(δ)) − Ω₁(¹³C^(γ)) − Ω₂(¹H^(γ2)) “Cross peak” 15. Ω₀(¹³C^(δ)) −Ω₁(¹³C^(γ)) − Ω₂(¹H^(γ3)) “Cross peak” 16. Ω₀(¹³C^(δ)) − Ω₁(¹³C^(β)) −Ω₂(¹H^(β2/β3)) “Relay peak” 17. Ω₀(¹³C^(δ)) + Ω₁(13C^(δ)) “Diagonalpeak” 18. Ω₀(¹³C^(δ)) + Ω₁(¹³C^(γ)) “Cross peak” 19. Ω₀(¹³C^(δ)) +Ω₁(13C^(β)) “Relay peak” 20. Ω₀(¹³C^(δ)) − Ω₁(13C^(δ)) “Diagonal peak”21. Ω₀(¹³C^(δ)) − Ω₁(¹³C^(γ)) “Cross peak” 22. Ω₀(¹³C^(δ)) − Ω₁(¹³C^(β))“Relay peak”

FIG. 27 depicts the r.f. pulse scheme of GFT (5,3)D HC(C)C—CH.Rectangular 90° and 180° pulses are indicated by thin and thick verticalbars, respectively, and phases are indicated above the pulses. Where nor.f. phase is marked, the pulse is applied along x. High-power 90° pulselengths are: 5.5 is for ¹H, 15.0 μs for ¹³C and 38 μs for ¹⁵N. ¹³Cdecoupling during t₁(¹H) is achieved using a (90°_(x)-180°_(y)-90°_(x))composite pulse. The SEDUCE sequence is used for decoupling of ¹³C′during t₁(¹³C) and t₂(¹³C) (r.f field strength=1 kHz). WURST is used fordecoupling of ¹³C during acquisition. The duration of ¹H spin-lock purgepulses for suppression of the water line are: SL_(x), 4.9 ms; SL_(y):2.6 ms; SL_(x)′: 1.6 ms. The ¹H carrier position is placed at 0 ppmbefore the first 90° ¹H pulse and then switched to 4.77 ppm after thesecond 90° ¹H pulse. The ¹³C and ¹⁵N r.f. carrier positions are set to43 ppm (for aliphatic spin system assignments) and 118.5 ppm,respectively. ¹H-frequency labeling at a ¹H resonance frequency of 600MHz is achieved in a semi constant-time fashion with t₁ ^(a)(0)=1.7 ms,t₁ ^(b)(0)=1 μs, t₁ ^(c)(0)=1.701 ms, Δt₁ ^(a)=33.3 μs, Δt₁ ^(b)×19.3μs, Δt₁ ^(c)=−14 μs. Hence, the fractional increase of the semiconstant-time period with t₁ equals to λ=1+Δt₁ ^(c)/Δt₁ ^(a)=0.58. Theduration and strengths of the pulsed z-field gradients (PFGs) are: G1(500 μs, 6 G/cm); G2 (500 μs, 12 G/cm); G3 (500 μs, 11 G/cm); G4 (2.0ms, 22 G/cm); G5 (100 μs, 12 G/cm); G6 (2.0 ms, 15 G/cm); G7 (500 μs, 6G/cm). All PFG pulses are of rectangular shape. The delays are: τ₁=350μs, τ₂=2.65 ms, τ₃=τ₅=7.0 ms, τ₄=7.0 ms, τ_(a)=850 μs, τ_(b)=1.65 ms andτ_(c)=2.5 ms. Phase cycling: φ₁=x; φ₁=x, −x; φ₃=x, −x; φ₄=x; φ₅=y;φ₆(receiver)=x, −x. Quadrature detection in t₁(¹³C/¹H) and t₂(¹³C) isaccomplished by altering the phases φ₄ and φ₅, respectively, accordingto States-TPPI. GFT NMR super phase-cycle for recording the 4 basicspectra: φ₁=x,y; φ₂=2(x),2(y). For acquisition of central peaks derivedfrom ¹³C steady state magnetization, a second data set with φ₁=−x iscollected. The sum and the difference of the two resulting data setsgenerate two subspectra containing the central peaks and peak pairs.

FIGS. 28(a)-(b) depict the r.f. pulse schemes of PFG-PEPsensitivity-enhanced L-2D [¹³C,¹H]-HSQC (FIG. 28(a)) and L-2D[¹³C,¹H]-TROSY (FIG. 28(b)). 90° ¹H pulses with “rising” and “falling”shapes represent, respectively, E-BURP2 and time-reversed E-BURP2 pulses(Geen et al., J. Magn. Reson. 93:93-141 (1991), which is herebyincorporated by reference in its entirety) of 1.1 ms duration. Thesepulses are applied 2.5 ppm upfield of the ¹H carrier, which is placed onthe water line, and serve to selectively flip ¹H^(aliphatic)/¹H₂Omagnetization. Shaped 180° pulses on ¹³C represent REBURP pulses(Cavanagh et al., Protein NMR Spectroscopy: Principles and PracticeAcademic Press: San Diego (1996), which is hereby incorporated byreference in its entirety) of 610 μs duration. Carbon spins aredecoupled during acquisition with GARP (γB₁/2π=2.5 kHz) (Cavanagh etal., Protein NMR Spectroscopy: Principles and Practice Academic Press:San Diego (1996), which is hereby incorporated by reference in itsentirety). For FIG. 28(a): λ=1.3 ms, T=8 ms, ε=0.3 ms; φ₁={y},φ₂={x,−x}, φ₃={x}, φ_(rec)={x,−x}; G₁: 4 G/cm, 0.5 ms; G₂: 20.6 G/cm, 1ms; G_(C): 24 G/cm, 1.6 ms; G_(H): 24 G/cm, 0.4 ms. Quadrature detectionin t₁ is achieved by recording a second scan with φ₃={−x} and G_(C)inverted. For FIG. 28(b): λ=1.3 ms, T′=T−λ=6.7 ms; φ₁={x,−x}, φ₂={−y},φ_(rec)={x,−x}; G₁: 9 G/cm, 0.8 ms; G₂: 7 G/cm, 1 ms; G_(C): 18.8 G/cm,1 ms; G_(H): 4.7 G/cm. Quadrature detection in t, is achieved byrecording a second scan with φ₂={y} and G_(C) inverted.

FIG. 29 illustrates the calculated relative sensitivity (I_(SE)/I₀)resulting from employment of PFG-PEP (¹H frequency: 750 MHz; gradientecho length 2ε: 200 μs). For comparison, the dashed line is obtained for2ε=600 μs, indicating that careful optimization of this parameter isadvantageous for large systems.

FIGS. 30(a)-(b) show SN_(t) plotted versus t_(rel) for threerepresentative cross peaks. Filled (open) symbols and solid (dashed)lines correspond to spectra acquired with (without) L-optimization. FIG.30(a) shows data from 2D [¹³C,¹H]-HSQC spectra recorded at 20° C. FIG.30(b) shows data from 2D [¹³C,¹H]-TROSY spectra recorded at 4° C. withsuppression of signals arising from ¹³C polarization.

FIG. 31 illustrates the calculated relative sensitivity of TROSY overnon-TROSY in ¹H^(aromatic)—¹³C^(aromatic) correlation experiments withct ¹³C^(aromatic) frequency labeling at a ¹H resonance frequency of 750MHz. Solid and dashed lines correspond, respectively, to ct evolutionperiods of 13.5 ms and 4.5 ms. The latter is preferably used forimplementing L-GFT (4,3)D HCCH (FIG. 32; see Example 8).

FIG. 32 depicts the r.f. pulse scheme of L-GFT-TROSY (4,3)D HCCH. 90°and 180° pulses are represented by thin and thick vertical bars.Selective 90° ¹H pulses with “rising” and “falling” shapes are 1.1 ms(at 750 MHz) E-BURP2 and time-reversed E-BURP2 pulses (Geen et al., J.Magn. Reson. 93:93-141 (1991), which is hereby incorporated by referencein its entirety) applied at 2 ppm. Those “flip” ¹H^(aliphatic)/¹H₂Omagnetization while ¹H^(aromatic) magnetization is along z. Duringreverse INEPT, “flip-back” pulses are not required since (i) hard ¹Hpulses yield a 720° rotation of ¹H magnetization and (ii) selective 180°¹³C^(aromatic) REBURP pulses (Geen et al., J. Magn. Reson. 93:93-141(1991), which is hereby incorporated by reference in its entirety) of610 μs duration (at 750 MHz) decouple ¹H^(aliphatic) from¹³C^(aliphatic). Phases of ¹H r.f. pulses are adjusted such that¹H^(aliphatic)/¹H₂O magnetization is along +z at the beginning of t₃.Decoupling of ³C^(aromatic) during t₃ is accomplished using GARP(γB₁/2π=2.5 kHz) (Cavanagh et al., Protein NMR Spectroscopy: Principlesand Practice Academic Press: San Diego (1996), which is herebyincorporated by reference in its entirety). Delays: λ=1.3 ms, κ=1.5 ms,T=T′=2.25 ms, δ=T−κ+t₁/2, ε=0.3 ms. ¹H⁽¹⁾ shift evolution during t₁ isimplemented in a semi ct manner with t_(1,max)=2T, t₁ ^(a)(0)=λ, t₁^(b)(0)=1 μs, t₁ ^(c)(0)=λ+1 μs, and Δt₁ ^(a)=t₁/2, Δt₁ ^(b)=Δt₁^(a)+Δt₁ ^(c), Δt₁ ^(c)=−λt₁/2T. Quadrature detection in t₂(¹³C⁽²⁾) isachieved with sensitivity enhancement (G_(C) is inverted with a 180°shift for φ₇); in t₁(¹³C⁽¹⁾;¹H⁽¹⁾), φ₄ is altered according toStates-TPPI (Cavanagh et al., Protein NMR Spectroscopy: Principles andPractice Academic Press: San Diego (1996), which is hereby incorporatedby reference in its entirety). PFGs: G₁(0.5 ms, 11 G/cm), G₂(1, 13),G₃(0.5, 21), G₄(0.5, 11), G_(C)(1.2, 24), G_(H) (0.3, −24). Phasecycling: φ₁={x}, φ₂={−y, y}, φ₃={8(−y), 8(y)}, φ₄={x, −y, −x, y},φ₅={4(x), 4(−x)}, φ₆={8(x), 8(−x)}, φ₇={x}, φ_(rec)={2(x), 2(−x)}. AnS³-filter (Meissner et al., J. Magn. Reson. 139:447-450 (1999), which ishereby incorporated by reference in its entirety) implements TROSY: theblack-and-white 180° pulse on ¹H is applied only every odd step of thephase cycle. To decouple ¹J(¹³C^(γ)-¹³C^(β)) for enhancing signals atΩ(¹³C^(γ)) in central peak subspectra (FIG. 33), the 180° pulse duringt₁(¹³C⁽²⁾) is applied with (Cavanagh et al., Protein NMR Spectroscopy:Principles and Practice Academic Press: San Diego (1996), which ishereby incorporated by reference in its entirety) γB₁=Δω/√3 (Δω isdifference between ¹³C^(aromatic) carrier and average ¹³C^(β) shift).GFT NMR phase-cycle: φ₁=x,y,−x,−y to obtain basic subspectra from ¹H andcentral peak subspectra from ¹³C polarization (Kim et al., J. Am. Chem.Soc. 125:1385-1393 (2003), which is hereby incorporated by reference inits entirety). For L-GFT (4,3)D HCCH: δ=κ, the black-and-white 180°pulse during t₁(¹³C⁽²⁾) is at high power and a ¹³C 90° pulse before PFGG₀ is added. Phase cycling: φ₂={y}, φ₃={4(y),4(−y)}, φ₄={x,−x}, φ₅={x,x, −x, −x}, φ₆={4(x), 4(−x)}, φ₇={x}, φ_(rec)={x,−x}. GFT NMR phasecycle: φ₁=x,y for basic subspectra; the central peak subspectrum isrecorded by omitting ¹H⁽¹⁾ shift evolution.

FIG. 33 shows [ω₁(¹³C⁽¹⁾;¹H⁽¹⁾,ω₃(¹H⁽²⁾)]-strips taken along the GFTdimension of L-GFT-TROSY (4,3)D HCCH recorded at 750 MHz for 21 kDa HR41with t_(rel)=1 s. Peaks belong to the slowly flipping ring of Tyr 90.Central peaks arising from ¹³C^(γ/ζ) polarization are depicted in blue.

FIG. 34 depicts cross sections taken along the GFT dimension from L-GFT(4,3)D HCCH (solid traces) and GFT (4,3)D HCCH (dotted traces) acquiredfor 11 kDa protein MaR11 in 25 min each.

FIG. 35 indicates NOEs and chemical shifts which are measured in (4,3)D[HC ^(ali)/HN]-NOESY-[CH^(ali)/NH], provided that central peaks aredetected in 3D [H]-NOESY-[CH^(ali)/CH^(aro)/NH]. The proton from whichthe NOE originates and the proton on which the signal is detected areshown, respectively, in dashed and bold circles. For the heteronuclei(depicted in black) which are attached to the detected proton, thechemical shift is measured in both (4,3)D [HC^(ali)/HN]-NOESY-[CH^(ali)/NH] and 3D [H]-NOESY-[CH^(ali)/CH^(aro)/NH].The heteronuclei attached to the “originating” proton are shown in grey.The boxes around ¹⁵N and ¹³C^(aliphatic) indicate that these shifts aremeasured in shift doublet subspectra of (4,3)D [HC^(ali)/HN]-NOESY-[CH^(ali)/NH], thereby providing 4D NOESY information.For clarity, transposed NOEs are not indicated.

FIGS. 36(a)-(b) depict r.f. pulse schemes employed for acquisition ofNOESY data. FIG. 36(a) shows detection of shift doublets in (4,3)D [HC^(ali)/HN]-NOESY-[CH^(ali)/NH], while FIG. 36(b) shows detection ofshifts in 3D [H]-NOESY-[CH^(ali)/CH^(aro)/NH]. Both schemes are derivedfrom simultaneous 3D ¹⁵N/¹³C^(aliphatic)-resolved [¹H,¹H]-NOESY (Xia etal., J. Biomol. NMR 27:193-203 (2003), which is hereby incorporated byreference in its entirety). Rectangular 90° and 180° pulses areindicated by thin and thick vertical bars, respectively, and phases areindicated above the pulses. Where no r.f. phase is marked, the pulse isapplied along x. High-power 90° pulse lengths are: 9.0 μs for ¹H, 17.0μs for ¹³C, and 40 μs for ¹⁵N. WURST (Cavanagh et al., Protein NMRSpectroscopy Academic Press: San Diego (1996), which is herebyincorporated by reference in its entirety) is used for decoupling of ¹³Cduring acquisition. WALTZ16 (Cavanagh et al., Protein NMR SpectroscopyAcademic Press: San Diego (1996), which is hereby incorporated byreference in its entirety) is employed to decouple ¹⁵N (r.f.=1.70 kHz)during acquisition. ¹³C decoupling during indirect ¹H chemical shiftevolution is achieved using a (90°_(x)-180°_(y)-90°_(x)) composite pulse(Cavanagh et al., Protein NMR Spectroscopy Academic Press: San Diego(1996), which is hereby incorporated by reference in its entirety).SEDUCE (Cavanagh et al., Protein NMR Spectroscopy, Academic Press: SanDiego (1996), which is hereby incorporated by reference in its entirety)is used for decoupling of ¹³C, during t₁(¹H/¹³C/¹⁵N) and t₂(¹³C/¹⁵N)(r.f. field strength=1 kHz). The duration of ¹H spin-lock purge pulsesapplied immediately after acquisition to improve suppression of thewater line (Xia et al., J. Biomol. NMR 27:193-203 (2003), which ishereby incorporated by reference in its entirety) are: SL_(x), 4.9 ms;SL_(y): 2.6 ms. The ¹H r.f. and ¹⁵N carrier positions are set to 4.78ppm and 118 ppm, respectively. For t₂(¹³C/¹⁵N), sampling starts at1/(2·SW( ¹³C/¹⁵N)) to ensure 180° first order phase correction (Cavanaghet al., Protein NMR Spectroscopy Academic Press: San Diego (1996), whichis hereby incorporated by reference in its entirety). Parametersspecific for the individual r.f. pulse schemes: For FIG. 36(a): thescaling factor was set to κ=0.5, and the ¹³C carrier position is set to36 ppm. ¹H-¹³C INEPT rely on (90°_(x)-180°_(y)-90°_(x)) composite pulses(Cavanagh et al., Protein NMR Spectroscopy Academic Press: San Diego(1996), which is hereby incorporated by reference in its entirety), andthe ¹H-¹³C INEPT delays are set to 3.9 ms (corresponding to a¹J_(CHaliphatic)˜130 Hz). ¹H-frequency labeling (at a ¹H resonancefrequency of 600 MHz) is achieved in a semiconstant-time fashion(Cavanagh et al., Protein NMR Spectroscopy Academic Press: San Diego(1996), which is hereby incorporated by reference in its entirety) witht₁ ^(a)(0)=1.9 ms, t₁ ^(b)(0)=1.0 μs, t₁ ^(c)(0)=2.5 ms, Δt₁ ^(a)=40 μs,Δt₁ ^(b)=35 μs, Δt₁ ^(c)=−15 μs. Hence, the fractional increase of thesemiconstant-time period with t₁ equals to λ=1+Δt₁ ^(c)/Δt₁ ^(a)=0.63.The duration and strengths of the rectangular pulsed z-field gradients(PFGs) are: G₁ (3 ms, 8 G/cm); G₂ (0.5 ms, 6 G/cm); G₃ (4 ms, 30 G/cm);G₄ (3 ms, −20 G/cm); G₅ (0.5 ms, 8 G/cm); G₆ (3.0 ms, 4 G/cm); G₇ (1.0ms, 8 G/cm). The delays are: τ₁=2.0 ms, τ₂=0.4 ms, Σ₃=2.4 ms. The mixingtime was set to τ_(m)=70 ms. Phase cycling: φ₁=x, −x; φ₂=x; φ₃=2(x),2(−x); φ₄(receiver)=x, −x, −x, x. Quadrature detection in t₁(¹H/¹³C/¹⁵N)and t₂(¹³C/¹⁵N) is accomplished by altering the phases φ₂ and φ₃,respectively, according to States-TPPI (Cavanagh et al., Protein NMRSpectroscopy Academic Press: San Diego (1996), which is herebyincorporated by reference in its entirety). GFT NMR phase-cycle forrecording the two basic spectra: φ₁=x, y. For FIG. 36(b): simultaneousinversion of ¹³C^(aliphatic) and ¹³C^(aromatic) spins during ¹H—¹³CINEPT is achieved using adiabatic 180° ¹³C r.f. pulses of 1.0 msduration (Cavanagh et al., Protein NMR Spectroscopy Academic Press: SanDiego (1996), which is hereby incorporated by reference in itsentirety), and the INEPT delay is tuned to a compromise value of ½¹J_(CH)=3.4 ms (corresponding to ¹J_(CHaliphatic)<¹J_(CH)=150Hz<¹J_(CHaromatic)) to allow simultaneous detection of NOEs on aliphaticand aromatic protons. The ¹³C carrier position is initially set to 70ppm and shifted to 36 ppm at the time point indicated by the first arrowand shifted back to 70 ppm at the time point indicated by the secondarrow. Bloch simulations show that the loss of sensitivity for thearomatic signals that arise from off-resonance effects of the tworectangular 90° pulses applied at a ¹³C carrier position of 36 ppm isless than −30% at 600 MHz ¹H resonance frequency. [At higher fieldstrengths, it is advantageous to minimize off-resonance effects byplacing the ¹³C carrier between aliphatic and aromatic resonances (at˜70 ppm) and employing time proportional phase incrementation (Cavanaghet al., Protein NMR Spectroscopy Academic Press: San Diego (1996);Szyperski et al., J. Magn. Reson. B108:197-203 (1995), which are herebyincorporated by reference in their entirety) to shift the ¹³C carrierposition to 36 ppm. At 900 MHz, for example, sensitivity losses at theedges of the ¹³C spectral range, i.e. for methyl groups and downfieldaromatic resonances, are then limited to ˜25%.]. The spectral widthsalong ω₂ are: ω₂(¹⁵N)=1,680 Hz, ω₂(¹³C^(aliphatic),¹³C^(aromatic))=4,300Hz. This ensures that NOEs detected on aromatic protons are aliasedalong ω₂(¹³C^(aliphatic),¹³C^(aromatic)) and, provided that a 180° firstorder phase correction is applied, have opposite sign than NOEs detectedon amide protons to facilitate assignment. Moreover, mutual cancellationof these two types of NOEs is avoided. The duration and strengths of therectangular pulsed z-field gradients (PFGs) are: G₁ (3 ms, 6 G/cm); G₂(3 ms, 4 G/cm); G₃ (1 ms, 8 G/cm); G₄ (0.5 ms, 8 G/cm); G₅ (4 ms, 30G/cm); G₆ (3 ms, −20 G/cm); G₇ (0.5 ms, 6 G/cm). The delays are: τ₁=1.2ms, τ₂=0.2 ms, τ₃=2.4 ms. The mixing time was set to τ_(m)=70 ms. Phasecycling: φ₁=2(x), 2(−x); φ₂=x, −x; φ₃=x; φ₄ (receiver)=x, −x, −x, x.Quadrature detection in t₁(¹H) and t₂(¹³C/¹⁵N) is accomplished byaltering the phases φ₁ and φ₂, respectively, according to States-TPPI(Cavanagh et al., Protein NMR Spectroscopy Academic Press: San Diego(1996), which is hereby incorporated by reference in its entirety).

FIGS. 37(a)-(d) illustrate resonance assignment based on GFT NMRexperiments (Tables 10 and 11) exemplified for protein YqfB. Panel (a)shows [ω₁(¹³C^(α);¹³C^(αβ)),ω₃(¹H^(N))]-strips taken from (4,3)D C ^(αβ)C ^(α)(CO)NHN (labeled with “a1”) and (4,3)D HNNC ^(αβ) C ^(α) (labeledwith “a2”). The strips were taken at ω₂(¹⁵N) (the ¹⁵N chemical shiftsare indicated at the bottom of the strips) of residues 57 to 60(referred to as residue i), and are centered along ω₃(¹H^(N)) abouttheir backbone ¹H^(N) shifts. Along ω₁(¹³C^(α);¹³C^(αβ)), peaks areobserved at Ω(¹³C^(α))±Ω(¹³C^(α/β)) of residue i−1 in “a1” and ofresidue i in “a2” (in addition, peaks originating from residue i−1 areobserved in “a2” if transfer via ²J_(NCα) is sufficiently effective).Ω(X) (X=¹³C^(α),¹³C^(β)) denotes the offset relative to the carrierposition [during t₁(¹³C^(αβ)), the ¹³C carrier frequency is placed at 43ppm; during t₁(¹³C^(α)), ¹³C^(α) is detected in quadrature and thecarrier frequency is placed at 56 ppm; see FIGS. S7 and S9 of Atreya etal., Proc. Natl. Acad. Sci. USA 101:9642-9647 (2004), which is herebyincorporated by reference in its entirety]. The composite plot of stripson the left was taken from the GFT subspectrum comprising peaks atΩ(¹³C^(α))+Ω(¹³C^(α)) (labeled as 1, 3, 5, 7) and Ω(¹³C^(α))+Ω(¹³C^(β))(labeled as 2, 4, 6, 8), and the composite plot on the right was takenfrom the subspectrum comprising peaks at Ω(¹³C^(α))−Ω(¹³C^(α)) (1, 3, 5,7) and Ω(¹³C^(α))−Ω(¹³C^(β)) (2, 4, 6, 8) (the type of linearcombination of chemical shifts is indicated above the composite plots).The combined use of (4,3)D C ^(αβ) C ^(α)(CO)NHN/HNNC ^(αβ) C ^(α)yields three sequential “walks” along the polypeptide backbone which areindicated by dashed lines [note: peaks at Ω(¹³C^(α))−Ω(¹³C^(α)) on theright are all located at the carrier position (43 ppm) and do notprovide connectivities]. Peaks were sequentially assigned to the¹³C^(α/β) shifts of Ala 57 (1, 2), Thr 58 (3, 4), Ser 59 (5, 6), and Thr60 (7, 8) after ¹³C′_(i-1),¹⁵N_(i),¹H^(N)-spin system identification wasaccomplished in the second- and third-order central peak spectra B13-B15of (5,2)D HACACONHN (Kim et al., J. Am. Chem. Soc. 125:1385-1393 (2003),which is hereby incorporated by reference in its entirety), whichrepresents (3,2)D HNNCO and thus encodes 3D HNNCO (Cavanagh et al.,Protein NMR Spectroscopy Academic Press: San Diego (1996), which ishereby incorporated by reference in its entirety) spectral information.This is indicated in panel (b) which shows composite plots of stripstaken from (5,2)D HACACONHN (Kim et al., J. Am. Chem. Soc. 125:1385-1393(2003), which is hereby incorporated by reference in its entirety). This(5,2)D experiment is used to sequence specifically assign ¹H^(α) and¹³C′ shifts after having obtained the sequence specific assignments of¹³C^(α/β), ¹⁵N, and ¹H^(N) from (4,3)D C ^(αβ) C ^(α)(CO)NHN/HNNC ^(αβ)C ^(α). The signals in panel (b) arise from magnetization transfer from¹H^(α) of His 32 to ¹H^(N) of Phe 33. The eight basic spectra (labeledB1-B8) encode the chemical shifts of ¹Hα_(i-1),¹³C^(α)_(i-1),¹³C′_(i-1), and ¹⁵N_(i) in a single GFT dimension (ω₁). Due tothe particular choice for quadrature detection of ¹⁵N and central peakdetection (Kim et al., J. Am. Chem. Soc. 125:1385-1393 (2003), which ishereby incorporated by reference in its entirety), combination ofchemical shifts are registered as Ω₀±Ω₁±Ω₂±Ω₃ with Ω₀=Ω(¹⁵N),Ω₁=Ω(¹³C′), Ω₂=Ω(¹³C^(α)) and Ω₃=Ω(¹H^(α)). Note that the ppm-scalealong Ω₁ is defined by the type of nucleus detected in quadrature (¹⁵Nin this case). As a result, the jointly sampled chemical shifts ofdifferent types of nuclei (¹H and ¹³C in this case) are scaled up by theratio of the gyromagnetic ratios (for example, the ¹H chemical shifts inppm are scaled up 10-times on the ¹⁵N ppm scale). Specifically, thelinear combinations observed in subspectra B1-B8 are: B1 [Ω₀+Ω₁+Ω₂+Ω₃];B2 [Ω₀−Ω₁+Ω₂+Ω₃]; B3 [Ω₀+Ω₁−Ω₂+Ω₃]; B4 [Ω₀−Ω₁−Ω₂+Ω₃]; B5 [Ω₀+Ω₁+Ω₂−Ω₃];B6 [Ω₀−Ω₁+Ω₂−Ω₃]; B7 [Ω₀+Ω₁−Ω₂−Ω₃]; B8 [Ω₀−Ω₁−Ω₂−Ω₃]. To resolvepotential shift degeneracies, first-order central peak spectra areacquired (B9-B12) comprising peaks at: B9 [Ω₀+Ω₁+Ω₂]; B10 [Ω₀−Ω₁+Ω₂];B11 [Ω₀+Ω₁−Ω₂]; B12 [Ω₀−Ω₁−Ω₂], second-order central peaks (B13-B14)comprise peaks at B13 [Ω₀+Ω₁] and B14 [Ω₀−Ω₁], and third-order centralpeaks (B15) are signals of 2D [¹⁵N,¹H]-HSQC at Ω₀. Panel (c) showsassignment of aliphatic side chains exemplified for Ile 85. On the left,two composite plots show strips taken from the basic subspectraproviding Ω(¹³C)+Ω(¹H) (labeled B1) and Ω(¹³C)−Ω(¹H) (labeled B2) alongthe GFT dimension ω₁ (Table 10). On the right, a composite plot (labeledB3) shows strips taken from the central peak spectrum of (4,3)D {umlautover (HC)}CH providing Ω(¹³C) along ω₁ [that is, 3D (H)CCH information(Cavanagh et al., Protein NMR Spectroscopy Academic Press: San Diego(1996), which is hereby incorporated by reference in its entirety)]. Foraliphatic spin system identification, sums and differences of shifts ofcovalently attached ¹³C and ¹H nuclei (Table 10) are delineated in B1and B2, while ¹³C shifts are matched in B3 (indicated by dashed lines).Sequence-specific assignments are inferred from ¹H^(α) and ¹³C^(αβ)shifts assigned in (4,3)D HNNC ^(αβ) C ^(α)/C ^(αβ) C ^(α)(CO)NHN(Atreya et al., Proc. Natl. Acad. Sci. USA 101:9642-9647 (2004), whichis hereby incorporated by reference in its entirety) and (5,2)DHACACONHN (Kim et al., J. Am. Chem. Soc. 125:1385-1393 (2003), which ishereby incorporated by reference in its entirety) as described in thedescription for panels (a) and (b). The five [ω₁(¹³C;¹H),ω₃(¹H)]-stripswere taken along ω₂(¹³C) at the shifts of ¹³C^(α), ¹³C^(β), ¹³C^(γ1),¹³C^(γ2), and ¹³C^(δ1) of Ile 85 (indicated at the bottom of the stripsof B3). The peaks encode along ω₁ linear combinations of the followingshifts: ¹³C^(α)/¹H^(α) (labeled as 1), ¹³C^(β)/¹H^(β) (2),¹³C^(γ12,γ13)/¹H^(γ12,γ13) (3), ¹³C^(γ2)/¹H^(γ2) (4) and¹³C^(δ1)/¹H^(δ1) (5). Panel (d) depicts the identification of aromaticspin systems in (4,3)D HCCH demonstrated for Tyr 89. On the left, twocomposite plots show strips taken from basic subspectra providingΩ(¹³C)+Ω(¹H) (labeled B1) and Ω(¹³C)−Ω(¹H) (labeled B2). The compositeplot shown on the right (labeled B3) shows strips taken from the centralpeak spectrum of (4,3)D HCCH providing Ω(¹³C) along ω₁. Aromatic spinsystem identification was accomplished in a manner similar to thatdescribed in the legend of panel (c) for aliphatic spin systems, andsequence-specific assignments were inferred from observation (Wüthrich,NMR of proteins and Nucleic Acids Wiley: New York (1986), which ishereby incorporated by reference in its entirety) of intraresidue NOEs.The two [ω₁(¹³C;¹H),ω₃(¹H)]-strips from each of the three subspectrumwere taken along ω₂(¹³C) at the shifts of ¹³C^(δ) and ¹³C^(ε) of Tyr 89(indicated at the bottom of the strips of B3). The peaks encode along(ok linear combinations of the following shifts: ¹³C^(δ)/¹H^(δ) (labeledas 1) and ¹³C^(ε)/¹H^(ε) (2) (since Ω(¹H^(δ))=7.2 ppm and Ω(¹H^(ε))=6.7ppm, the separation of peaks labeled with 1 in B1 and B2 appears to besimilar to the separation of peaks labeled with 2).

FIGS. 38(a)-(b) are [I_(uni),I_(ave)] plots calculated with the programQUEEN (Nabuurs et al., J. Am. Chem. Soc. 125:12026-12034 (2003), whichis hereby incorporated by reference in its entirety) of upper distancelimit constraints derived from the 3D [H]-NOESY-[CH^(ali)/CH^(aro)/NH]peak list (see Examples 18, 21, and 24) used to calculate the referenceYqfB structure (1TE7). In FIG. 38(a), constraints obtained in 3D[H]-NOESY-[CH^(ali)/CH^(aro)/NH] based on chemical shift data only aredepicted as green circles, additional constraints assigned withreference to shift doublet data sets I and II of (4,3)D [HC^(ali)/HN]-NOESY-[CH^(ali)/NH] are shown as red and blue circles,respectively. Aromatic and other aliphatic constraints which could beassigned only with reference to an (initial) structure are displayed asblack and grey circles, respectively. The distribution of the circlesshows that chemical shift based NOE assignment is, as expected, notdependent on the information content of an NOE. In FIG. 38(b),additional constraints, which were identified by the program CYANA(Herrmann et al., J. Mol. Biol. 319:209-227 (2002), which is herebyincorporated by reference in its entirety) in the first cycle with aprobability of >85%, are depicted as red circles while those assignedbased on shifts are in green [as in FIG. 38(a)], and others aredisplayed in grey. Comparison with (a) reveals significant bias towardidentification of constraints with lower information content. Theaverage I_(uni)/I_(total) and I_(ave)/I_(total) are 0.071% and 0.679%for the red constraints (total: 72) in FIG. 38(a), which were identifiedwith chemical shift doublet data set I. The corresponding values for thered constraints (total: 40) in FIG. 38(b), which were assigned withCYANA, are only 0.011% and 0.254%, respectively.

In FIG. 39, the sensitivity of each of the peaks forming a shift doubletregistered in (4,3)D [HC ^(ali)/HN]-NOESY-[CH ^(ali)/NH] relative to thecorresponding central peak [in %] is plotted as a function of thecorrelation time for the isotropic overall rotational tumbling of arigid protein. Doublets encoding Ω(¹⁵N) and Ω(¹³C^(aliphatic)) arerepresented by solid and dashed lines, respectively. Since doubletsarise from an in-phase splitting of central peaks, the relativesensitivity is a priori reduced to 50%. The curves reflect further T₂spin relaxation losses that occur during the additional simultaneous[¹⁵N,¹H]/[¹³C,¹H]-HSQC module (FIG. 36(a)). The transverse relaxationrates of ¹HN, ¹⁵N, ¹³C^(aliphatic) and ¹H^(aliphatic) as a function ofthe protein correlation time, τ_(r), were taken from Wagner, J. Biomol.NMR 3:375-385 (1993), which is hereby incorporated by reference in itsentirety. The relative sensitivity predicted for YqfB is given andτ_(r)=7.7 is indicated by a vertical dotted line.

FIGS. 40(a)-(b) illustrate the chemical shift based NOE assignment in(4,3)D [HC ^(ali)/HN]-NOESY-[CH^(ali)/NH] acquired with 3D[H]-NOESY-[CH^(ali)/CH^(aro)/NH] for central peak detection. Panel (a)shows the ¹⁵N-resolved part: [ω₁,ω₃(¹H^(N))]-strips taken from the shiftdoublet sub-spectrum exhibiting peaks at Ω(¹H)+Ω(X) along ω₁ (X=¹⁵N,¹³C;shown on the left and indicated as b1), from the shift doubletsubspectrum exhibiting peaks at Ω(¹H)−Ω(X) along ω₁ (X=¹⁵N,¹³C;indicated in the middle as b2) and the central peak subspectrum (3D[H]-NOESY-[CH^(ali)/CH^(aro)/NH]; indicated on the right as b3). Signalswere detected on the backbone amide proton of Leu 78. Four peaks areshown in red which are overlapped in the central peak spectrum. Thesepeaks are well resolved and can be unambiguously assigned directly fromchemical shifts in the shift doublet subspectra (data set I recorded in30 hours). Assignments: NOEs between H^(N) of Leu 78 and (1) H^(β2) ofLeu 78, (2) CH₃ ^(γ2) of Thr 77, (3) CH₃ ^(β) of Ala 71, and (4) H^(γ)of Leu 78. Panel (b) shows the ¹³C-resolved part:[ω₁,ω₃(¹H^(aliphatic))]-strips taken from the same subspectra. Signalswere detected on α-proton of residue Thr 58. Two long-range NOEs areshown in red which can be unambiguously assigned directly from chemicalshifts in the shift doublet subspectra. Assignments: NOEs between H^(α)of Thr 58 and (1) CH₂ ^(γ) of Ile 98, (2) H^(α) of Ile 98.

FIGS. 41(a)-(c) illustrate the precision (FIG. 41(a)) and accuracy(FIGS. 41(b)-(c)) of comparative YqfB structure calculations (r.m.s.d.values were taken from Table 13). In FIG. 41(a), r.m.s.d. valuesreflecting precision were calculated for the backbone heavy atoms N,C^(α) and C′ (on the left) and all heavy atoms (on the right) ofresidues 4-101, and are displayed on vertical scales. In FIG. 41(b) (forbackbone) and FIG. 41(c) (for heavy atoms), plots of r.m.s.d. valuesreflecting accuracy were calculated between mean coordinates of the 20DYANA conformers of a given structure and the mean coordinates of the 20conformers of the reference structure (1TE7), and are displayed versusthe precision r.m.s.d. values provided in FIG. 41(a). The dashed lineabove the diagonal represents the equality r.m.s.d.(accuracy)=r.m.s.d.(precision)+r.m.s.d.(reference structure). Structuresbelow this line can be considered to be ‘accurate’, since the allowedconformational subspaces overlap (see text). The dashed line below thediagonal represents the equalityr.m.s.d.(accuracy)=r.m.s.d.(precision)−r.m.s.d.(reference structure).Structures below this line can be considered to be ideally suited forfurther refinement, since the allowed conformational space of theinitial structure largely includes the allowed space of the referencestructure. Codes (FIG. 42; Table 13): ×reference structure (1TE7); +reference structure calculated after omission of stereo-specificassignments; ▪: initial structure calculated with NOEs assigned in 3D[H]-NOESY-[CH^(ali)/CH^(aro)/NH] based on chemical shift data only; ●and ∘: initial structures calculated with additional NOEs assigned in 3D[H]-NOESY-[CH^(ali)/CH^(aro)/NH] with reference to shift doublet datasets I and II of (4,3)D [HC ^(ali)/HN]-NOESY-[CH^(ali)/NH] (FIG. 40); ▾:intial structure calculated with the program CYANA (Güntert et al., J.Mol. Biol. 273:283-298 (1997); Herrmann et al., J. Mol. Biol.319:209-227 (2002); Güntert, Methods Mol. Biol. 278:347-372 (2004),which are hereby incorporated by reference in their entirety) (1^(st)cycle); ▴ and Δ: final structures calculated with the program CYANA whenstarting with constraint input used for ● and ∘. The “refinementtrajectory” (see Example 25) is indicated by dotted arrows; thebifurcation represents the availability or non-availability ofstereospecific assignments (Table 12).

FIGS. 42(a)-(f) depict a survey of YqfB structures. FIG. 42(a) is thereference structure (PDB ID 1TE7; code in FIG. 42: ×) FIG. 42(b) is thereference structure calculated after omission of stereospecificassignments (+). FIG. 42(c) is the initial structure calculated withNOEs assigned in 3D [H]-NOESY-[CH^(ali)/CH^(aro)/NH] based on chemicalshift data only (▪). FIG. 42(d) is the initial structure calculated withadditional NOEs assigned in 3D [H]-NOESY-[CH^(ali)/CH^(aro)/NH] withreference to shift doublet data sets I of (4,3)D [HC^(ali)/HN]-NOESY-[CH^(ali)/NH] (●). FIG. 42(e) is the same as in FIG.42(d) but with shift doublet data set II (∘). FIG. 42(f) is the initialstructure calculated with the program CYANA (1^(st) cycle out of 7;Herrmann et al., J. Mol. Biol. 319:209-227 (2002), which is herebyincorporated by reference in its entirety) with TALOS dihedral angleconstraints and intraresidue, sequential, and medium-range distanceconstraints as input (▾). The 20 DYANA conformers with the lowestresidual target function value were chosen to represent the NMR solutionstructures. These conformers were superimposed for minimal r.m.s.d. ofbackbone heavy atoms N, C^(α), and C′ of residues 4-101 and the heavyatoms of the best defined side-chains (Table 12). The figure wasgenerated using the program Molmol (Koradi et al., J. Mol. Graphics14:51-55 (1996), which is hereby incorporated by reference in itsentirety).

FIG. 43 shows composite plots of [ω₁(¹H; ¹⁵N/¹³C^(aliph)), ω₂(¹H)]strips taken from the basic and first order central peak spectra of(4,2)D ¹⁵N/¹³C^(aliph) resolved [¹H,¹H] NOESY. The basic spectra(labeled “b1”-“b4”), the first order central peak spectra (labeled“b5”-“b6”) and the second order central peak spectra (labeled “b7”) arecentered on the respective ω₂(¹H) chemical shifts. Strips have beentaken at ω₁(¹H^(N)) chemical shift of residue Thr 67. The peaks labeled1-28 correspond to the following linear combination of chemical shiftsalong ω₁ (i≡Thr 67; i−1≡Thr 67):

-   -   1. Ω₀(¹H^(N) _(i))+Ω₁(¹⁵N_(i))/2.0+Ω₂(¹⁵N_(i))/2.0    -   2. Ω₀(¹H^(α) _(i-1))+Ω₁(¹⁵N_(i))/2.0+Ω₂(¹³C^(α) _(i-1))/2.0    -   3. Ω₀(¹H^(γ2) _(i))+Ω₁(¹⁵N_(i))/2.0+Ω₂(¹³C^(γ2) _(i))/2.0    -   4. Ω₀((¹H^(δ1) _(i-1))₃)+Ω₁(¹⁵N_(i))/2.0+Ω₂(¹³C^(δ1) _(i-1))/2.0    -   5. Ω₀(¹H^(N) _(i))+Ω₁(¹⁵N_(i))/2.0−Ω₂(¹⁵N_(i))/2.0    -   6. Ω₀(¹H^(α) _(i-1))+Ω₁(¹⁵N_(i))/2.0−Ω₂(¹³C^(α) _(i-1))/2.0    -   7. Ω₀(¹H^(γ2) _(i))+Ω₁(¹⁵N_(i))/2.0−Ω₂(¹³C^(γ2) _(i))/2.0    -   8. Ω₀((¹H^(δ1) _(i-1))₃)+Ω₁(¹⁵N_(i))/2.0−Ω₂(¹³C^(δ1) _(i-1))/2.0    -   9. Ω₀(¹H^(N) _(i))−Ω₁(¹⁵N_(i))/2.0+Ω₂(¹⁵N_(i))/2.0    -   10. Ω₀(¹H^(α) _(i-1))−Ω₁(¹⁵N_(i))/2.0+Ω₂(¹³C^(α) _(i-1))/2.0    -   11. Ω₀(¹H^(γ2) _(i))−Ω₁(¹⁵N_(i))/2.0+Ω₂(¹³C^(γ2) _(i))/2.0    -   12. Ω₀((¹H^(δ1) _(i-1))₃−Ω₁(¹⁵N_(i))/2.0+Ω₂(¹³C^(δ1) _(i-1))/2.0    -   13. Ω₀(¹H^(N) _(i))−Ω₁(¹⁵N_(i))/2.0−Ω₂(¹⁵N_(i))/2.0    -   14. Ω₀(¹H^(α) _(i-1))−Ω₁(¹⁵N_(i))/2.0−Ω₂(¹³C^(α) _(i-1))/2.0    -   15. Ω₀(¹H^(γ2) _(i))−Ω₁(¹⁵N_(i))/2.0−Ω₂(¹³C^(γ2) _(i))/2.0    -   16. Ω₀((¹H^(δ1) _(i-1))₃−Ω₁(¹⁵N_(i))/2.0−Ω₂(¹³C^(δ1) _(i-1))/2.0    -   17. Ω₀(¹H^(N) _(i))+Ω₁(¹⁵N_(i))/2.0    -   18. Ω₀(¹H^(α) _(i-1))+Ω₁(¹⁵N_(i))/2.0    -   19. Ω₀(¹H^(γ2) _(i))+Ω₁(¹⁵N_(i))/2.0    -   20. Ω₀((¹H^(δ1) _(i-1))₃)+Ω₁(¹⁵N_(i))/2.0    -   21. Ω₀(¹H^(N) _(i))−Ω₁(¹⁵N_(i))/2.0    -   22. Ω₀(¹H^(α) _(i-1))−Ω₁(¹⁵N_(i))/2.0    -   23. Ω₀(¹H^(γ2) _(i))−Ω₁(¹⁵N_(i))/2.0    -   24. Ω₀((¹H^(δ1) _(i-1))₃)−Ω₁(¹⁵N_(i))/2.0    -   25. Ω₀(¹H^(N) _(i))    -   26. Ω₀(¹H^(α) _(i-1))    -   27. Ω₀(¹H^(γ2) _(i))    -   28. Ω₀((¹H^(δ1) _(i-1))₃)

FIG. 44 depicts the r.f. pulse scheme of (4,2)D¹⁵N/¹³C^(aliphatic)-resolved [¹H,¹H]-NOESY. Rectangular 90° and 180°pulses are indicated by thin and thick vertical bars, respectively, andphases are indicated above the pulses. Where no r.f. phase is marked,the pulse is applied along x. High-power 90° pulse lengths are: 9.0 μsfor ¹H, 17.0 μs for ¹³C and 40 μs for ¹⁵N. SEDUCE is used for decouplingof ¹³C′ during t₁(¹³C/¹⁵N) and t₂(¹³C/¹⁵N) (r.f. field strength=1 kHz).WURST is used for decoupling of ¹³C during acquisition and ¹³Cdecoupling during t₁(¹H) is achieved using a (90°_(x)-180°_(y)-90°_(x))composite pulse. WALTZ16 is employed to decouple ¹⁵N (r.f.=1.70 kHz)during acquisition. The duration of ¹H spin-lock purge pulses appliedimmediately after acquisition for suppression of the water line are:SL_(x), 4.9 ms; SL_(y): 2.6 ms. The ¹H r.f. carrier position is placedat 4.78 ppm. The ¹⁵N and ¹³C carrier positions are set to 118.0 ppm and36 ppm, respectively. ¹H-frequency labeling (at a ¹H resonance frequencyof 600 MHz) is achieved in a semi constant-time fashion with t₁^(a)(0)=ms, t₁ ^(b)(0)=μs, t₁ ^(c)(0)=ms, Δt₁ ^(a)=μs, Δt₁ ^(b)=μs, Δt₁^(c)=μs. Hence, the fractional increase of the semi constant-time periodwith t₁ equals to λ=1+Δt₁ ^(c)/Δt₁ ^(a)=0.58. The duration and strengthsof the pulsed z-field gradients (PFGs) are: G₁ (1 ms, 22 G/cm); G₂ (500μs, 6 G/cm); G₃ (1 ms, 20 G/cm); G₄ (500 μs, 6 G/cm); G₅ (2.0 ms, 15G/cm); G₆ (2.0 ms, 15 G/cm); G₇ (2.0 ms, 20 G/cm); G₈ (2.0 ms, −20G/cm). All PFG pulses are of rectangular shape. The delays are: τ₁=1.8ms, τ₂=0.6 ms, τ₃=2.4 ms, τ_(m)=70 ms. Phase cycling: φ₁=x; φ₂=x;φ₃=x,−x; φ₄=x,−x; φ₅ (receiver)=x,−x,−x,x. Quadrature detection int₁(¹H) is accomplished by altering the phase φ₂ according toStates-TPPI. GFT-NMR super phase-cycling scheme for recording the twobasic spectra is: φ₁=x,y.

FIG. 45 shows composite plots of [ω₁(¹H; ¹⁵N/¹³C^(aliph)), ω₂(¹H)]strips taken from the basic and first order central peak spectra of(3,2)D ¹⁵N/¹³C^(aliph) resolved [¹H, ¹H] NOESY. The basic spectra(labeled “b1”-“b2”) and the first order central peak spectra (labeled“b3”) are centered on the respective ω₂(¹H) chemical shifts. Strips havebeen taken at ω₁(¹HN) chemical shift of residue Thr 67. The peakslabeled 1-12 correspond to the following linear combination of chemicalshifts along ω₁ (i≡Thr 67; i−1≡Thr 67):

-   -   1. Ω₀(¹H^(N) _(i))+Ω₁(¹⁵N_(i))/2.0    -   2. Ω₀(¹H^(α) _(i-1))+Ω₁(¹⁵N_(i))/2.0    -   3. Ω₀(¹H^(γ2) _(i))+Ω₁(¹⁵N_(i))/2.0    -   4. Ω₀((¹H^(δ1) _(i-1))₃)+Ω₁(¹⁵N_(i))/2.0    -   5. Ω₀(¹H^(N) _(i))−Ω₁(¹⁵N_(i))/2.0    -   6. Ω₀(¹H^(α) _(i-1))−Ω₁(¹⁵N_(i))/2.0    -   7. Ω₀(¹H^(γ2) _(i))−Ω₁(¹⁵N_(i))/2.0    -   8. Ω₀((¹H^(δ1) _(i-1))₃)−Ω₁(¹⁵N_(i))/2.0    -   9. Ω₀(¹H^(N) _(i))    -   10. Ω₀(¹H^(α) _(i-1))    -   11. Ω₀(¹H^(γ2) _(i))    -   12. Ω₀((¹H^(δ1) _(i-1))₃)

FIG. 46 depicts the r.f. pulse scheme of (3,2)D¹⁵N/¹³C^(aliphatic)-resolved [¹H,¹H]-NOESY. Rectangular 90° and 180°pulses are indicated by thin and thick vertical bars, respectively, andphases are indicated above the pulses. Where no r.f. phase is marked,the pulse is applied along x. High-power 90° pulse lengths are: 9.0 μsfor ¹H, 17.0 μs for ¹³C and 40 μs for ¹⁵N. SEDUCE is used for decouplingof ¹³C′ during t₁(¹³C/¹⁵N) and t₂(¹³C/¹⁵N) (r.f. field strength=1 kHz).WURST is used for decoupling of ¹³C during acquisition and ¹³Cdecoupling during t₁(¹H) is achieved using a (90°_(x)-180°_(y)-90°_(x))composite pulse. WALTZ16 is employed to decouple ¹⁵N (r.f.=1.70 kHz)during acquisition. The duration of ¹H spin-lock purge pulses appliedimmediately after acquisition for suppression of the water line are:SL_(x), 4.9 ms; SL_(y): 2.6 ms. The ¹H r.f. carrier position is placedat 4.78 ppm. The ¹⁵N and ¹³C carrier positions are set to 118.0 ppm and36 ppm, respectively. The duration and strengths of the pulsed z-fieldgradients (PFGs) are: G₁ (1 ms, 22 G/cm); G₂ (1 ms, 8 G/cm); G₃ (1 ms,20 G/cm); G₄ (500 μs, 6 G/cm); G₅ (2.0 ms, 15 G/cm); G₆ (2.0 ms, 15G/cm). All PFG pulses are of rectangular shape. The delays are: τ₁=1.8ms, τ₂=0.6 ms, τ₃=2.4 ms, τ_(m)=70 ms. Phase cycling: φ₁=2(x), 2(y);φ₂=x, −x; φ₃=4(x), 4(y), 4(−x), 4(−y); φ₄(receiver)=x,−x,−x,x,−y,y,y,−y,−x,x,x,−x,y,−y,−y,y. Quadrature detectionin t₁(¹H) is accomplished by altering the phase φ₁ according toStates-TPPI. GFT NMR super phase-cycling scheme for recording the twobasic spectra is: φ₂=x,y.

FIG. 47 depicts the r.f. pulse scheme of J-GFT (6,2)D(H^(α)—C^(α)—CO)—N—HN for the measurement of RDCs. Rectangular 90° and180° pulses are indicated by thin and thick vertical bars, respectively,and phases are indicated above the pulses. Where no r.f. phase ismarked, the pulse is applied along x. The shaded portion of the sequenceis shown as an expansion in the figure with different modulation schemesof the coupling constants. The high power 90° pulse lengths were: 5.8 μsfor ¹H and 15.4 μs for ¹³C, and 38 μs for ¹⁵N. The ¹⁵N r.f. carrier isset to 120.9 ppm. The ¹³C carrier is set to 56 ppm initially and shiftedto 176 ppm before the first pulse on ¹³C′. Pulses on ¹³C prior to t₁^(a) are applied at high power, and ¹³C coupling during the ¹H—¹³C^(α)INEPT (Cavanagh et al., Protein NMR Spectroscopy Academic Press: SanDiego, Calif. (1996), which is hereby incorporated by reference in itsentirety) is achieved using a (90°_(x)-180°_(y)-90°_(x)) compositepulse. Subsequently, the 90° and 180° pulse lengths of ¹³C^(α) areadjusted to 51.5 μs and 46 μs (at a ¹H resonance frequency of 600 MHz),respectively, to minimize perturbation of the ¹³C′ spins. A six-pulsecomposite sequence (Shaka, Chem. Phy. Lett. 120:201-205 (1985), which ishereby incorporated by reference in its entirety) is used tosimultaneously invert/refocus ¹³C^(α)/¹³C′ magnetization during¹³C^(α)—¹³C′ polarization transfer. The width of the 90° SEDUCE pulses(Cavanagh et al., Protein NMR Spectroscopy Academic Press: San Diego,Calif. (1996), which is hereby incorporated by reference in itsentirety) applied to ¹³C′ pulse is 200 μs and the corresponding 180°pulses are applied with same power. WALTZ16 (Cavanagh et al., ProteinNMR Spectroscopy Academic Press: San Diego, Calif. (1996), which ishereby incorporated by reference in its entirety) is employed todecouple ¹H (r.f. field strength=9.2 kHz) during the heteronuclearmagnetization transfers as well as to decouple ¹⁵N during acquisition(r.f.=1.78 kHz). The off-resonance SEDUCE sequence (Cavanagh et al.,Protein NMR Spectroscopy Academic Press: San Diego, Calif. (1996), whichis hereby incorporated by reference in its entirety) is used fordecoupling of ¹³C^(α) during the ¹⁵N chemical shift evolution period(adiabatic decoupling of aliphatic ¹H during signal detection could beemployed for enhancing sensitivity (Vander Kooi et al., J. Biomol. NMR15:335-338 (1999), which is hereby incorporated by reference in itsentirety). The ¹H r.f. carrier is placed at the position of the solventline at 4.78 ppm. The duration and strengths of the pulsed z-fieldgradients (PFGs) are: G1 (1 ms, 24 G/cm); G2 (100 μs, 8 G/cm); G3 (1 ms,20 G/cm); G4 (500 μs, 8 G/cm); G5 (1.0 ms, 20 G/cm); G6 (1.0 ms, 20G/cm); G7 (1.25 ms, 30 G/cm); G8 (500 μs, 8 G/cm); G9 (125 μs, 29.5G/cm). All PFG pulses are of rectangular shape. The delays are:τ_(a)=1.7 ms, τ₁=4.5 ms, τ₂=24.0 ms, τ₃=27.3 ms, τ₄=2.7 ms, τ₅=4.6 ms,τ₆=1.0 ms, τ_(N)=30 ms. Phase cycling: φ₁=x, −x; φ₂=2(x), 2(−x); φ₃=x;φ₄(receiver)=x, −x. A sensitivity enhancement scheme (Kay et al., J. Am.Chem. Soc. 114:10663-10665 (1992), which is hereby incorporated byreference in its entirety) is employed, i.e., the sign of G7 is invertedin concert with a 180° shift of φ₅. Quadrature detection of t₁(¹⁵N) isachieved via gradient selection of coherences using G7. GFT NMR superphase-cycling scheme for recording the basic spectra is describedbriefly below: (i) Detection of ¹J(¹H^(α)—¹³C^(α)): Cosine modulation:t₁ ^(a)/6.0 = t₁/6.0 + 1.7 ms Sine modulation: t₁ ^(a)/6.0 = t₁/6.0 (ii)Detection of ¹J(¹³C^(α)—¹³C′): Cosine modulation: t₁ ^(b)/2.0 = t₁/2.0 +4.5 ms Sine modulation: t₁ ^(b)/2.0 = t₁/2.0 (iii) Detection of¹J(¹⁵N—¹³C′): Cosine modulation: Scheme (a) or (b) Sine modulation:Scheme (c) or (d) (iv) Detection of ¹J(¹⁵N—¹H): Cosine modulation:Scheme (a) or (c) Sine modulation: Scheme (b) or (d)The central peak spectra are acquired by successively omitting thecoupling evolution in the order (i) to (iv) shown above, using the samer.f. pulse scheme.

FIG. 48 is a schematic diagram of the r.f. pulse module used fordetecting the cosine and sine modulation of the transfer amplitude for agiven pair of nuclei, I-S, in J-GFT (6,2)D (H^(α)—C^(α)—CO)—N—HN. Thismodule is repeatedly incorporated for simultaneous measurement ofmultiple RDCs during polarization transfers (FIG. 47). Rectangular 90°and 180° pulses are indicated by thin and thick vertical bars,respectively. The delay ‘τ’ is set to ½J_(IS), where J_(IS) is theone-bond scalar coupling constant under isotropic conditions. Therelevant product operator terms at points a and b are described inExample 26.

FIG. 49 is a schematic depiction of the peak pattern observed in J-GFT(6,2)D (H^(α)—C^(α)—CO)—N—HN spectra. The subspectra are grouped intobasic, first-, second-, and third-order central peaks. The fourth-ordercentral peak is represented by a peak in the 2D [¹⁵N—¹H] HSQC. Thelinear combination of the couplings observed in each group of subspectrais shown.

FIG. 50 shows composite plots of [ω₁(¹⁵N; ¹J_(HN), ¹J_(NC′), ¹J_(C) ^(α)_(C′), ¹J_(H) ^(α) _(C) ^(α)), ω₂(¹H)] strips taken from the basicspectra (labeled b1-b16), first order central peak spectra (labeledb17-b24), second order central peak spectra (labeled b25-b28), thirdorder central peak spectra (labeled b29-b30) and fourth order centralpeak spectra (labeled b31) of the (6,2)D (¹H^(α)—¹³C^(α)—¹³CO)—N—HNrecorded for Z-domain in (A) isotropic and (B) liquid-crystalline (Pf1phage aligned) medium at 25° C. The strips are centered about theirbackbone ¹HN chemical shifts. As an example, strips corresponding toω₂(¹H^(N)) chemical shifts for residue Leu 32 of protein Z-domain areshown. The following notation has been used for representing one-bondscalar and residual dipolar coupling constants, where the subscript ‘i’refers to the residue number:

In (A): J_(HN)=¹J_(H(i)N(i)); J_(NC′)=¹J_(N(i)C′(i-1)); J_(C′) ^(α)_(C′)=¹J_(C) ^(α) _((i-1)C′(i-1));

-   -   J_(H) ^(α) _(C) ^(α)=¹J_(H) ^(α) _((i-1)C) ^(α) _((i-1));        In (B): J_(HN)=¹J_(H(i)N(i))+¹J^(D) _(H(i)N(i));        J_(NC′)=¹J_(N(i)C(i-1)′)+¹J^(D) _(N(i)C(i)′);    -   J_(C) ^(α) _(C′)=¹J_(C) ^(α) _((i-1)C′(i-1))+¹J^(D) _(C) ^(α)        _((i-1)C′(i-1)); J_(H) ^(α) _(C) ^(α=) ¹J_(H) ^(α) _((i-1)C)        ^(α) _((i-1))+¹J^(D) _(H) ^(α) _((i-1)C) ^(α) _((i-1)))        Peaks labeled 1-31 correspond to the following linear        combination of chemical shifts in both (A) and (B):    -   1. Ω₀(¹⁵N)+J_(HN)/2.0+¹J_(NC′)/2.0+J_(C) ^(α) _(C′)/2.0+J_(H)        ^(α)C^(α)/6.0    -   2. Ω₀(¹⁵N)+J_(HN)/2.0+¹J_(NC′)/2.0+J_(C) ^(α) _(C′) /2.0−J _(H)        ^(α) _(C) ^(α)/6.0    -   3. Ω₀(¹⁵N)+J_(HN)/2.0+¹J_(NC′)/2.0−J_(C) ^(α) _(C′)/2.0+J_(H)        ^(α) _(C) ^(α)/6.0    -   4. Ω₀(¹⁵N)+J_(HN)/2.0+1JNC′/2.0−J_(C) ^(α) _(C′)/2.0−J_(H) ^(α)        _(C) ^(α)/6.0    -   5. Ω₀(¹⁵N)+J_(HN)/2.0−1JNC′/2.0+J_(C) ^(α) _(C′)/2.0+J_(H) ^(α)        _(C) ^(α)/6.0    -   6. Ω₀(¹⁵N)+J_(HN)/2.0−1JNC′/2.0+J_(C) ^(α) _(C′)/2.0−J_(H) ^(α)        _(C) ^(α)/6.0    -   7. Ω₀(¹⁵N)+J_(HN)/2.0−1JNC′/2.0−J_(C) ^(α) _(C′)/2.0+J_(H) ^(α)        _(C) ^(α)/6.0    -   8. Ω₀(¹⁵N)+J_(HN)/2.0−1JNC′/2.0−J_(C) ^(α) _(C′)/2.0−J_(H) ^(α)        _(C) ^(α)/6.0    -   9. Ω₀(¹⁵N)−J_(HN)/2.0+1JNC′/2.0+J_(C) ^(α) _(C′)/2.0+J_(H) ^(α)        _(C) ^(α)/6.0    -   10. Ω₀(¹⁵N)−J_(HN)/2.0+1JNC′/2.0+J_(C) ^(α) _(C′)/2.0−J_(H) ^(α)        _(C) ^(α)/6.0    -   11. Ω₀(¹⁵N)−J_(HN)/2.0+1JNC′/2.0−J_(C) ^(α) _(C′)/2.0+J_(H) ^(α)        _(C) ^(α)/6.0    -   12. Ω₀(¹⁵N)−J_(HN)/2.0+1JNC′/2.0−J_(C) ^(α) _(C′)/2.0−J_(H) ^(α)        _(C) ^(α)/6.0    -   13. Ω₀(¹⁵N)−J_(HN)/2.0−1JNC′/2.0+J_(C) ^(α) _(C′)/2.0+J_(H) ^(α)        _(C) ^(α)/6.0    -   14. Ω₀(¹⁵N)−J_(HN)/2.0−1JNC′/2.0+J_(C) ^(α) _(C′)/2.0−J_(H) ^(α)        _(C) ^(α)/6.0    -   15. Ω₀(¹⁵N)−J_(HN)/2.0−1JNC′/2.0−J_(C) ^(α) _(C′)/2.0+J_(H) ^(α)        _(C) ^(α)/6.0    -   16. Ω₀(¹⁵N)−J_(HN)/2.0−1JNC′/2.0−J_(C) ^(α) _(C′)/2.0−J_(H) ^(α)        _(C) ^(α)/6.0    -   17. Ω₀(¹⁵N)+J_(HN)/2.0+1JNC′/2.0+J_(C) ^(α) _(C′)/2.0    -   18. Ω₀(¹⁵N)+J_(HN)/2.0+¹J_(NC′)/2.0−J_(C) ^(α) _(C′)/2.0    -   19. Ω₀(¹⁵N)+J_(HN)/2.0−¹J_(NC′)/2.0+J_(C) ^(α) _(C′)/2.0    -   20. Ω₀(¹⁵N)+J_(HN)/2.0−¹J_(NC′)/2.0−J_(C) ^(α) _(C′)/2.0    -   21. Ω₀(¹⁵N)−J_(HN)/2.0+¹J_(NC′)/2.0+J_(C) ^(α) _(C′)/2.0    -   22. Ω₀(¹⁵N)−J_(HN)/2.0+¹J_(NC′)/2.0−J_(C) ^(α) _(C′)/2.0    -   23. Ω₀(¹⁵N)−J_(HN)/2.0−¹J_(NC′)/2.0+J_(C) ^(α) _(C′)/2.0    -   24. Ω₀(¹⁵N)−J_(HN)/2.0−¹J_(NC′)/2.0−J_(C) ^(α) _(C′)/2.0    -   25. Ω₀(¹⁵N)+J_(HN)/2.0+¹J_(NC′)/2.0    -   26. Ω₀(¹⁵N)+J_(HN)/2.0−¹J_(NC′)/2.0    -   27. Ω₀(¹⁵N)−J_(HN)/2.0+¹J_(NC′)/2.0    -   28. Ω₀(¹⁵N)−J_(HN)/2.0−¹J_(NC′)/2.0    -   29. Ω₀(¹⁵N)+J_(HN)/2.0    -   30. Ω₀(¹⁵N)−J_(HN)/2.0    -   31. Ω₀(15N)

DETAILED DESCRIPTION OF THE INVENTION

G²FT NMR: Design Principles, Theory, and Data Processing

The present application discloses novel “G²FT NMR experiments” in whichtwo G-matrix transformations are applied. This allows one to jointlysample shifts solely serving to provide increased resolution separatelyfrom those also providing sequential connectivities. As a result, oneobtains data sets in which spin system identification can be based on(3,2)D GFT NMR in the first GFT dimension, for example, while previouslydescribed peak patterns (Atreya et al., Proc. Natl. Acad. Sci. USA101:9642-9647 (2004), which is hereby incorporated by reference in itsentirety) for sequential assignment are retained in the second GFTdimension.

Previously described ¹⁵N,¹H^(N)-resolved triple resonance (4,3)D GFT NMRexperiments (Kim et al., J. Biomol. NMR 28:117-130 (2004); Atreya etal., Proc. Natl. Acad. Sci. USA 101:9642-9647 (2004), which are herebyincorporated by reference in their entirety) contain a single “GFTdimension” used for establishing sequential links based on ¹³C^(α/β)and/or ¹H^(α) shifts. In the second indirect dimension (the “resolvingdimension”) ¹⁵N shifts are measured, which solely serve to providesignal dispersion. In cases of high ¹⁵N—¹H^(N) shift degeneracy, overlapoccurs in this dimension. Spectral resolution can be improved if shiftsof other nuclei (e.g., ¹³C′_(i-1)) are measured in addition to ¹³C^(αβ)or ¹³C^(α)/¹H^(α) and ¹⁵N shifts in the indirect dimensions. This canserve to separate two spin systems which have degenerate ¹³C^(α)/¹³C^(β)or/and ¹⁵N/¹H^(N) shifts but non-degenerate ¹³C′_(i-1) chemical shifts.This can be accomplished in two ways: (i) jointly sample the ¹³C′_(i-1)shift in the GFT dimension of the (4,3)D experiments along with the¹³C^(α)/¹³C^(β) shifts, or (ii) jointly sample the ¹³C′_(i-1) shiftalong with the ¹⁵N shift in the resolving dimension. Importantly, thefirst approach “scrambles” the GFT peak pattern of the (4,3)Dexperiments, since the ¹³C′_(i-1) shifts are linearly combined withthose of ¹³C^(α) _(i)/¹³C^(β) _(i) and ¹³C^(α) _(i-1)/¹³C^(β) _(i-1). Onthe other hand, combining ¹³C′_(i-1) and ¹⁵N shifts allows one tojointly sample those shifts which solely serve to provide increasedresolution separately from those providing sequential connectivities.Then, each of the two indirect dimensions serve for joint sampling of adistinct set of shifts, and the processing of such data sets requiresemployment of two G-matrix transformations. Hence, these experiments arenamed “G²FT NMR” experiments. Such grouping of jointly sampled shifts(i) provides increased spectral resolution by increasing signaldispersion in both the indirect dimensions (See Atreya et al., Proc.Natl. Acad. Sci. USA 101:9642-9647 (2004), which is hereby incorporatedby reference in its entirety), (ii) allows one to pursue spin systemidentification based on 3D spectral information obtained from (3,2)D GFTNMR, (iii) allows one to match peak pattern (“C ^(αβ) C ^(α) or C ^(α) H^(α)-pattern”) manifested in the second GFT dimension in order toestablish sequential connectivites. To minimize loss of sensitivity,additional frequency labeling is preferably accomplished in a constanttime manner (Wüthrich, NMR of Proteins and Nucleic Acids Wiley: New York(1986), which is hereby incorporated by reference in its entirety)during delays required for magnetization transfer. This has twoadvantages: (i) no additional signal losses due to transverse relaxationoccur, and (ii) lines do not broaden because of the joint sampling ofmultiple shifts (Kim et al., J. Am. Chem. Soc. 125:1385-1393 (2003),which is hereby incorporated by reference in its entirety). Based onthese considerations, (5,3)D HN{N,CO}{C ^(αβ) C ^(α)} and (5,3)DHN{NCO}{C ^(αβ) C ^(α)} were designed. For systems with high¹³C^(α)/¹³C^(β) shift degeneracy, precluding efficient linking of spinssystems, (5,3)D HN{N,CO}{C ^(α) H ^(α)}/HN{NCO}{C ^(α) H ^(α)} weredesigned to additionally employ H^(α) shifts for establishing sequentialconnectivities. In the same spirit, one can combine ¹³C^(α) _(i/i-1) and¹⁵N shifts in the “resolving-dimension”. This offers an alternative wayto break spectral overlap in systems with very high shift degeneracy,and leads to the implementation of (5,3)D G²FT HN{NC ^(α)}{C ^(αβ) C^(α)} and HN{N(CO)C ^(α)}{C ^(αβ) C ^(α)}. A novel feature of (5,3)DG²FT HN{NC ^(α)}{C ^(αβ) C ^(α)} is that intraresidue and sequentialpeaks are located in different planes (since the ¹⁵N_(i) shift iscombined with ¹³C^(α) _(i/i-1)), that is, in cases of multiplesequential shift degeneracy, this experiment allows one to unambiguouslyconfirm the presence of both the intra- and sequential peaks associatedwith a given backbone NH moiety.

A (N,N-K)D GFT NMR experiment enables phase sensitive joint sampling ofK+1 chemical shifts in a single indirect dimension named the “GFTdimension” (Kim et al., J. Am. Chem. Soc. 125:1385-1393 (2003); Kim etal., J. Biomol. NMR 28:117-130 (2004); Atreya et al., Proc. Natl. Acad.Sci. USA 101:9642-9647 (2004), which are hereby incorporated byreference in their entirety). The other N−1 dimensions areconventionally sampled (Cavanagh et al., Protein NMR SpectroscopyAcademic Press: San Diego (1996), which is hereby incorporated byreference in its entirety). The joint sampling of K+1 chemical shiftevolution periods generates chemical shift multiplets with 2^(K)components located at Ω₀±Ω₁ . . . ±Ω_(K). These multiplets are editedinto 2^(K) different subspectra by G-matrix transformation (Kim et al.,J. Am. Chem. Soc. 125:1385-1393 (2003); Kim et al., J. Biomol. NMR28:117-130 (2004); Atreya et al., Proc. Natl. Acad. Sci. USA101:9642-9647 (2004), which are hereby incorporated by reference intheir entirety) of 2^(K) data sets each containing the chemical shiftmultiplets with a different in-phase/anti-phase pattern. Consideringboth real and an imaginary part of these 2^(K) data sets, a total of2^(K+1) data sets with varying sine and cosine modulation of shifts haveto be linearly combined. These can be written as a 2^(K+1) dimensionalvector: $\begin{matrix}{{\hat{S}(K)} \propto {\begin{bmatrix}C_{K} \\S_{K}\end{bmatrix} \otimes \ldots \otimes \begin{bmatrix}C_{l} \\S_{l}\end{bmatrix} \otimes \begin{bmatrix}C_{0} \\S_{0}\end{bmatrix}}} & (1)\end{matrix}$where c_(j)=cos(Ω_(j)t) and s_(j)=sin(Ω_(j)t), and t represents theevolution time in the indirect GFT dimension. The G-matrix is defined asa 2^(K)×2^(K+1) complex matrix (Kim et al., J. Am. Chem. Soc.125:1385-1393 (2003), which is hereby incorporated by reference in itsentirety): $\begin{matrix}{{\hat{G}(K)} = {\begin{bmatrix}1 & i \\1 & {- i}\end{bmatrix}_{1} \otimes \ldots \otimes \begin{bmatrix}1 & i \\1 & {- i}\end{bmatrix}_{K} \otimes \begin{bmatrix}1 & i\end{bmatrix}}} & (2)\end{matrix}$Multiplication of Ŝ(K) with the G-matrix according toT(K)=Ĝ(K)·Ŝ(K)  (3)yields the vector T(K) containing the edited subspectra. Those aresubsequently Fourier transformed yielding the desired 2^(K) frequencydomain subspectra (Kim et al., J. Am. Chem. Soc. 125:1385-1393 (2003),which is hereby incorporated by reference in its entirety).

The concept of GFT NMR data acquisition can be extended to the jointsampling of two sets of K′+1 and K″+1 different chemical shifts in twoseparate indirect dimensions (FIG. 1(a)). This results in shiftmultiplets with 2^(K′) and 2^(K″) components, respectively, in the twoGFT dimensions, yielding detection of a total of 2^(M) (M=K′+K″) linearcombination of chemical shifts [e.g., ω₁:(Ω_(0′)±Ω_(1′) . . .±Ω_(K′)){circle around (×)}ω₂:(Ω_(0″)±Ω_(1″) . . . ±Ω_(K″))] Those canbe edited into 2^(M) different subspectra as described in the following.

Each data set is collected by jointly incrementing K′+1 and K″+1 shiftsin the two GFT dimensions along with systematic variation of the phasesof r.f. pulses exciting spins of type i or j (i=1 . . . K′+1; j=1 . . .K″+1) between 0° and 90° in order to register both cosine and sinemodulated data sets (Kim et al., J. Am. Chem. Soc. 125:1385-1393 (2003),which is hereby incorporated by reference in its entirety) resulting ina total of 2^(K′+K″+2) data sets. These form a 2^(K′+1)*2^(K″+1)dimensional vector, which can be obtained by tensor product formationaccording to:Ŝ(K′, K″)=Ŝ(K′){circle around (×)}Ŝ(K″)  (4)Ŝ(K′, K″) shall be transformed by employment of G-matrix transformationinto T(K′, K″), which contains the 2^(M) (M=K′+K″) edited time domainsubspectra.With T(K′, K″)=T(K′){circle around (×)}T(K″)  (5)and Equation 3, one obtainsT(K′, K″)=[Ĝ(K′)·Ŝ(K′)]{circle around (×)}[Ĝ(K″)·Ŝ(K″)]  (6),which can be rearranged to: $\begin{matrix}{{T\left( {K^{\prime},K^{\prime\prime}} \right)} = {\left\lbrack {{\hat{G}\left( K^{\prime} \right)} \otimes {\hat{G}\left( K^{\prime\prime} \right)}} \right\rbrack \cdot \left\lbrack {{\hat{S}\left( K^{\prime} \right)} \otimes {S\left( K^{\prime\prime} \right)}} \right\rbrack}} & (7) \\{= {\left\lbrack {{\hat{G}\left( K^{\prime} \right)} \otimes {\hat{G}\left( K^{\prime\prime} \right)}} \right\rbrack \cdot {{\hat{S}\left( {K^{\prime},K^{\prime\prime}} \right)}.}}} & (8)\end{matrix}$Hence, Ĝ(K′, K″)=Ĝ(K′){circle around (×)}Ĝ(K″) represents the requiredG-matrix. In the case of K=K′=K″, Ĝ(K′, K″) corresponds to the tensorproduct of Ĝ(K) with itself, which can be written as G²(K)=Ĝ(K){circlearound (×)}Ĝ(K). This relation gives rise to the name “G²FT NMRexperiments”. If K′≠K″, the experiment has to be denoted as a “G′G″FT”NMR experiment” [e.g., (6,3)D {H ^(αβ) C ^(αβ) C ^(α)}{CON}HN; FIGS. 24and 25].

The data sets T(K′,K″) are Fourier transformed along both GFT dimensionsto yield the 2^(M) (N,N-M)D frequency domain subspectra. As examples,the real Ĝ(K′, K″) matrices used for processing the (5,3)D and (6,3)Ddata described in Examples 1 to 4 (FIG. 10; Table 1) are provided below.For (5,3)D: K′=K″=1 and for (6,3)D: K′=2; K″=1. Hence: $\begin{matrix}{{\hat{G}(1)} = {{\begin{pmatrix}1 & 0 & 0 & {- 1} \\0 & 1 & 1 & 0 \\1 & 0 & 0 & 1 \\0 & 1 & {- 1} & 0\end{pmatrix}\quad{\hat{G}(2)}} = \begin{pmatrix}1 & 0 & 0 & {- 1} & 0 & {- 1} & {- 1} & 0 \\0 & 1 & 1 & 0 & 1 & 0 & 0 & {- 1} \\1 & 0 & 0 & 1 & 0 & {- 1} & 1 & 0 \\0 & 1 & {- 1} & 0 & 1 & 0 & 0 & 1 \\1 & 0 & 0 & 1 & 0 & 1 & 1 & 0 \\0 & 1 & 1 & 0 & {- 1} & 0 & 0 & 1 \\1 & 0 & 0 & 1 & 0 & 1 & {- 1} & 0 \\0 & 1 & {- 1} & 0 & {- 1} & 0 & 0 & 1\end{pmatrix}}} & (9) \\{{{{\hat{G}\left( {1,1} \right)} = {{{\hat{G}(1)} \otimes {\hat{G}(1)}} = \begin{pmatrix}1 & 0 & 0 & {- 1} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {- 1} & 0 & 0 & 1 \\0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {- 1} & {- 1} & 0 \\1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {- 1} & 0 & 0 & {- 1} \\0 & 1 & {- 1} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {- 1} & 1 & 0 \\0 & 0 & 0 & 0 & 1 & 0 & 0 & {- 1} & 1 & 0 & 0 & {- 1} & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 1 & {- 1} & 0 & 0 & 1 & {- 1} & 0 & 0 & 0 & 0 & 0 \\1 & 0 & 0 & {- 1} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & {- 1} \\0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 \\0 & 1 & {- 1} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & {- 1} & 0 \\0 & 0 & 0 & 0 & 1 & 0 & 0 & {- 1} & {- 1} & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & {- 1} & {- 1} & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & {- 1} & 0 & 0 & {- 1} & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 1 & {- 1} & 0 & 0 & {- 1} & 1 & 0 & 0 & 0 & 0 & 0\end{pmatrix}}}\quad}\quad} & (10)\end{matrix}$${{\hat{G}\left( {2,1} \right)} = {{{\hat{G}(2)} \otimes {\hat{G}(1)}} = {\begin{pmatrix}1 & 0 & 0 & {- 1} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {- 1} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & {- 1} & 0 & 0 & 1 & {- 1} & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {- 1} & {- 1} & 0 & 0 & 0 & 0 & 0 & 0 & {- 1} & {- 1} & 0 & 0 & {- 1} & {- 1} & 0 & 0 & 0 & 0 & 0 \\1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {- 1} & 0 & 0 & {- 1} & 0 & 0 & 0 & 0 & {- 1} & 0 & 0 & {- 1} & {- 1} & 0 & 0 & {- 1} & 0 & 0 & 0 & 0 \\0 & 1 & {- 1} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {- 1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & {- 1} & 1 & 0 & 0 & {- 1} & 1 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 0 & 0 & {- 1} & 1 & 0 & 0 & {- 1} & 0 & 0 & 0 & 0 & 1 & 0 & 0 & {- 1} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {- 1} & 0 & 0 & 1 \\0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {- 1} & {- 1} & 0 \\0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {- 1} & 0 & 0 & {- 1} \\0 & 0 & 0 & 0 & 0 & 1 & {- 1} & 0 & 0 & 1 & {- 1} & 0 & 0 & 0 & 0 & 0 & 0 & 1 & {- 1} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {- 1} & 1 & 0 \\1 & 0 & 0 & {- 1} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & {- 1} & 0 & 0 & 0 & 0 & {- 1} & 0 & 0 & 1 & 1 & 0 & 0 & {- 1} & 0 & 0 & 0 & 0 \\0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & {- 1} & {- 1} & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & {- 1} & 0 & 0 & {- 1} & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\0 & 1 & {- 1} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & {- 1} & 0 & 0 & 0 & 0 & 0 & 0 & {- 1} & 1 & 0 & 0 & 1 & {- 1} & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 0 & 0 & {- 1} & {- 1} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & {- 1} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & {- 1} \\0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & {- 1} & {- 1} & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & {- 1} & 0 & 0 & {- 1} & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 \\0 & 0 & 0 & 0 & 0 & 1 & {- 1} & 0 & 0 & {- 1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & {- 1} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & {- 1} & 0 \\1 & 0 & 0 & {- 1} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {- 1} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & {- 1} & 1 & 0 & 0 & {- 1} & 0 & 0 & 0 & 0 \\0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {- 1} & {- 1} & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {- 1} & 0 & 0 & {- 1} & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\0 & 1 & {- 1} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {- 1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & {- 1} & 0 & 0 & 1 & {- 1} & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 0 & 0 & {- 1} & 1 & 0 & 0 & {- 1} & 0 & 0 & 0 & 0 & {- 1} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & {- 1} \\0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & {- 1} & {- 1} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & {- 1} & 0 & 0 & {- 1} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 \\0 & 0 & 0 & 0 & 0 & 1 & {- 1} & 0 & 0 & 1 & {- 1} & 0 & 0 & 0 & 0 & 0 & 0 & {- 1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & {- 1} & 0 \\1 & 0 & 0 & {- 1} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & {- 1} & 0 & 0 & 0 & 0 & 1 & 0 & 0 & {- 1} & {- 1} & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & {- 1} & {- 1} & 0 & 0 & 0 & 0 & 0 \\1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & {- 1} & 0 & 0 & {- 1} & 0 & 0 & 0 & 0 \\0 & 1 & {- 1} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & {- 1} & 0 & 0 & 0 & 0 & 0 & 0 & 1 & {- 1} & 0 & 0 & {- 1} & 1 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 0 & 0 & {- 1} & {- 1} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & {- 1} & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {- 1} & 0 & 0 & 1 \\0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & {- 1} & {- 1} & 0 & 0 & 0 & 0 & 0 & 0 & {- 1} & {- 1} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {- 1} & {- 1} & 0 \\0 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & {- 1} & 0 & 0 & {- 1} & 0 & 0 & 0 & 0 & {- 1} & 0 & 0 & {- 1} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {- 1} & 0 & 0 & {- 1} \\0 & 0 & 0 & 0 & 0 & 1 & {- 1} & 0 & 0 & {- 1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & {- 1} & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {- 1} & 1 & 0\end{pmatrix}\quad(11)}}}\quad$

The present invention discloses the following G²FT NMR experiments: (i)G²FT (5,3)D [HN{N,CO}{C ^(αβ) C ^(α)}]NMR; (ii) G²FT (5,3)D [HN{NCO}{C^(αβ) C ^(α)}] NMR; (iii) G²FT (5,3)D [HN{NC ^(α)}{C ^(αβ) C ^(α)}]NMR;(iv) G²FT (5,3)D [HN{N(CO)C ^(α)}{C ^(αβ) C ^(α)}]NMR; (v) G²FT (5,3)D[HN{N,CO}{C ^(α) H ^(α)}]NMR; (vi) G²FT (5,3)D [{H ^(α) C^(α)}{CON}HN]NMR; and (vii) G²FT (6,3)D [{H ^(αβ) C ^(αβ) C^(α)}{CON}{HN}] NMR. Experiments (i) and (iii), as well as (ii) and(iv), can form a pair to sequentially assign backbone ¹³C^(α) andsidechain ¹³C^(β) resonances in proteins. Experiment (v) and (vi) canform a pair to sequentially assign backbone ¹³C^(α) and ¹H^(α)resonances. Using these chemical shifts, experiment (vii) providesinformation on ¹H^(α/β) chemical shifts. The curly brackets groupjointly sampled shifts represented by underlined letters (Kim et al., J.Am. Chem. Soc. 125:1385-1393 (2003), which is hereby incorporated byreference in its entirety); in (5,3)D HN{N,CO}{C ^(αβ) C ^(α)} and(5,3)D HN{N,CO}{C ^(α) H ^(α)}, the comma indicates a bifurcated¹³C′_(i-1)←¹⁵N_(i)→¹³C^(α) _(i) transfer (Szyperski et al., J. Magn.Reson. B 109:229-233 (1995); Konrat et al., J. Biomol. NMR 15:309-313(1999); Szyperski et al., J. Am. Chem. Soc. 118:8147-8148 (1996);Szyperski et al., J. Biomol. NMR 11:387-405 (1998), which are herebyincorporated by reference in their entirety).

Thus, the present invention relates to a method of conducting a (5,3)dimensional (D) [HN{N,CO}{C ^(αβ) C ^(α)}] G-matrix Fouriertransformation (GFT) nuclear magnetic resonance (NMR) experiment. Themethod involves providing a sample, where the sample is a proteinmolecule having two consecutive amino acid residues, i−1 and i, and thechemical shift values for the following nuclei are measured: (1) α- andβ-carbons of amino acid residues i and i−1, ¹³C^(α/β) _(i/i-1); (2) apolypeptide backbone amide nitrogen of amino acid residue i, ¹⁵N_(i);(3) a polypeptide backbone carbonyl carbon of amino acid residue i−1,¹³C′_(i-1); and (4) a polypeptide backbone amide proton of amino acidresidue i, ¹H^(N) _(i). Next, radiofrequency pulses for a 5D FT NMRexperiment are applied to the sample. Then, a first set of 2 indirectchemical shift evolution periods of the 5D FT NMR experiment, ¹³C^(α/β)_(i/i-1) and ¹³C^(α) _(i/i-1), is selected. Next, the first set of 2indirect chemical shift evolution periods is jointly sampled in a firstindirect time domain dimension, t₁(¹³C^(α/β) _(i/i-1), ¹³C^(α)_(i/i-1)). Then, a second set of 2 indirect chemical shift evolutionperiods of the 5D FT NMR experiment, ¹⁵N_(i) and ¹³C′_(i-1), isselected. Next, the second set of 2 indirect chemical shift evolutionperiods is jointly sampled in a second indirect time domain dimension,t₂(¹⁵N_(i), ¹³C′_(i-1)). Then, NMR signals detected in a directdimension are independently cosine and sine modulated to generate 3Dbasic NMR spectra containing frequency domain signals having a chemicalshift multiplet with 4 components resulting from each of 2 chemicalshift doublet components in a first frequency domain dimension,ω₁(¹³C^(α/β), ¹³C^(α)), giving rise to 2 chemical shift doubletcomponents in a second frequency domain dimension, ω₂(¹⁵N, ¹³C′) therebyenabling phase-sensitive sampling of all jointly sampled 4 indirectchemical shift evolution periods. Finally, the 3D basic NMR spectra aretransformed into 3D phase-sensitively edited basic NMR spectra, wherethe 4 chemical shift multiplet components of the 3D basic NMR spectraare edited to yield 3D phase-sensitively edited basic NMR spectra havingindividual chemical shift multiplet components. One specific embodimentof this method, (5,3)D HN{N,CO}{C ^(αβ) C ^(α)}, involves applyingradiofrequency pulses for a 5D FT NMR experiment according to the schemeshown in FIG. 5.

Another aspect of the present invention relates to a method ofconducting a (5,3) dimensional (D) [HN{NCO}{C ^(αβ) C ^(α)}] G-matrixFourier transformation (GFT) nuclear magnetic resonance (NMR)experiment. The method involves providing a sample, where the sample isa protein molecule having two consecutive amino acid residues, i−1 andi, and the chemical shift values for the following nuclei are measured:(1) α- and β-carbons of amino acid residue i−1, ¹³C^(α/β) _(i-1); (2) apolypeptide backbone amide nitrogen of amino acid residue i, ¹⁵N_(i);(3) a polypeptide backbone carbonyl carbon of amino acid residue i−1,¹³C′_(i-1); and (4) a polypeptide backbone amide proton of amino acidresidue i, ¹H^(N) _(i). Next, radiofrequency pulses for a 5D FT NMRexperiment are applied to the sample. Then, a first set of 2 indirectchemical shift evolution periods of the 5D FT NMR experiment, ¹³C^(α/β)_(i-1) and ¹³C^(α) _(i-1), is selected. Next, the first set of 2indirect chemical shift evolution periods is jointly sampled in a firstindirect time domain dimension, t₁₍ ¹³C^(α/β) _(i-1), ¹³C^(α) _(i-1)).Then, a second set of 2 indirect chemical shift evolution periods of the5D FT NMR experiment, ¹⁵N_(i) and ¹³C′_(i-1), is selected. Next, thesecond set of 2 indirect chemical shift evolution periods is jointlysampled in a second indirect time domain dimension, t₂(¹⁵N_(i),¹³C′_(i-1)). Then, NMR signals detected in a direct dimension areindependently cosine and sine modulated to generate 3D basic NMR spectracontaining frequency domain signals having a chemical shift multipletwith 4 components resulting from each of 2 chemical shift doubletcomponents in a first frequency domain dimension, ω₁(¹³C^(α/β),¹³C^(α)), giving rise to 2 chemical shift doublet components in a secondfrequency domain dimension, ω₂(¹⁵N, ¹³C′), thereby enablingphase-sensitive sampling of all jointly sampled 4 indirect chemicalshift evolution periods. Finally, the 3D basic NMR spectra aretransformed into 3D phase-sensitively edited basic NMR spectra, wherethe 4 chemical shift multiplet components of the 3D basic NMR spectraare edited to yield 3D phase-sensitively edited basic NMR spectra havingindividual chemical shift multiplet components. One specific embodimentof this method, (5,3)D HN{NCO}{C ^(αβ) C ^(α)}, involves applyingradiofrequency pulses for a 5D FT NMR experiment according to the schemeshown in FIG. 6.

Another aspect of the present invention relates to a method ofconducting a (5,3) dimensional (D) [HN{NC ^(α)}{C ^(αβ) C ^(α))}]G-matrix Fourier transformation (GFT) nuclear magnetic resonance (NMR)experiment. The method involves providing a sample, where the sample isa protein molecule having two consecutive amino acid residues, i−1 andi, and the chemical shift values for the following nuclei are measured:(1) α- and β-carbons of amino acid residue i and i−1, ¹³C^(α/β)_(i/i-1); (2) a polypeptide backbone amide nitrogen of amino acidresidue i, ¹⁵N_(i); and (3) a polypeptide backbone amide proton of aminoacid residue i, ¹H^(N) _(i). Next, radiofrequency pulses for a 5D FT NMRexperiment are applied to the sample. Then, a first set of 2 indirectchemical shift evolution periods of the 5D FT NMR experiment, ¹³C^(α/β)_(i/i-1) and ¹³C^(α) _(i/i-1), is selected. Next, the first set of 2indirect chemical shift evolution periods is jointly sampled in a firstindirect time domain dimension, t₁(¹³C^(α/β) _(i/i-1), ¹³C^(α)_(i/i-1)). Then, a second set of 2 indirect chemical shift evolutionperiods of the 5D FT NMR experiment, ¹⁵N_(i) and ¹³C^(α) _(i/i-1), isselected. Next, the second set of 2 indirect chemical shift evolutionperiods is jointly sampled in a second indirect time domain dimension,t₂(¹⁵N_(i), ¹³C^(α) _(i/i-1)). Then, NMR signals detected in a directdimension are independently cosine and sine modulated to generate 3Dbasic NMR spectra containing frequency domain signals having a chemicalshift multiplet with 4 components resulting from each of 2 chemicalshift doublet components in a first frequency domain dimension,ω₁(¹³C^(α/β), ¹³C^(α)), giving rise to 2 chemical shift doubletcomponents in a second frequency domain dimension, ω₂(¹⁵N, ¹³C^(α)),thereby enabling phase-sensitive sampling of all jointly sampled 4indirect chemical shift evolution periods. Finally, the 3D basic NMRspectra are transformed into 3D phase-sensitively edited basic NMRspectra, where the 4 chemical shift multiplet components of the 3D basicNMR spectra are edited to yield 3D phase-sensitively edited basic NMRspectra having individual chemical shift multiplet components. Onespecific embodiment of this method, (5,3)D HN{NC ^(α)}{C ^(αβ) C ^(α)},involves applying radiofrequency pulses for a 5D FT NMR experimentaccording to the scheme shown in FIG. 13.

Another aspect of the present invention relates to a method ofconducting a (5,3) dimensional (D) [HN{N(CO)C ^(α)}{C ^(αβ) C ^(α)}]G-matrix Fourier transformation (GFT) nuclear magnetic resonance (NMR)experiment. The method involves providing a sample, where the sample isa protein molecule having two consecutive amino acid residues, i−1 andi, and the chemical shift values for the following nuclei are measured:(1) α- and β-carbons of amino acid residue i−1, ¹³C^(α/β) _(i-1); (2) apolypeptide backbone amide nitrogen of amino acid residue i, ¹⁵N_(i);and (3) a polypeptide backbone amide proton of amino acid residue i,¹H^(N) _(i). Next, radiofrequency pulses for a 5D FT NMR experiment areapplied to the sample. Then, a first set of 2 indirect chemical shiftevolution periods of the 5D FT NMR experiment, ¹³C^(α/β) _(i-1) and¹³C^(α) _(i-1), is selected. Next, the first set of 2 indirect chemicalshift evolution periods is jointly sampled in a first indirect timedomain dimension, t₁(¹³C^(α/β) _(i-1), ¹³C^(α) _(i-1)). Then, a secondset of 2 indirect chemical shift evolution periods of the 5D FT NMRexperiment, ¹⁵N_(i) and ¹³C^(α) _(i-1), is selected. Next, the secondset of 2 indirect chemical shift evolution periods is jointly sampled ina second indirect time domain dimension, t₂(¹⁵N_(i), ¹³C^(α) _(i-1)).Then, NMR signals detected in a direct dimension are independentlycosine and sine modulated to generate 3D basic NMR spectra containingfrequency domain signals having a chemical shift multiplet with 4components resulting from each of 2 chemical shift doublet components ina first frequency domain dimension, ω₁(¹³C^(α/β), ¹³C^(α)), giving riseto 2 chemical shift doublet components in a second frequency domaindimension, ω₂(¹⁵N, ¹³C^(α)), thereby enabling phase-sensitive samplingof all jointly sampled 4 indirect chemical shift evolution periods.Finally, the 3D basic NMR spectra are transformed into 3Dphase-sensitively edited basic NMR spectra, where the 4 chemical shiftmultiplet components of the 3D basic NMR spectra are edited to yield 3Dphase-sensitively edited basic NMR spectra having individual chemicalshift multiplet components. One specific embodiment of this method,(5,3)D HN{N(CO)C ^(α)}{C ^(αβ) C ^(α)}, involves applying radiofrequencypulses for a 5D FT NMR experiment according to the scheme shown in FIG.14.

Another aspect of the present invention relates to a method ofconducting a (5,3) dimensional (D) [HN{N,CO}{C ^(α) H ^(α)}] G-matrixFourier transformation (GFT) nuclear magnetic resonance (NMR)experiment. The method involves providing a sample, where the sample isa protein molecule having two consecutive amino acid residues, i−1 andi, and the chemical shift values for the following nuclei are measured:(1) α-carbon of amino acid residues i and i−1, ¹³C^(α) _(i/i-1); (2)α-proton of amino acid residues i and i−1, ¹H^(α) _(i/i-1); (3) apolypeptide backbone amide nitrogen of amino acid residue i, ¹⁵N_(i);(4) a polypeptide backbone carbonyl carbon of amino acid residue i−1,¹³C′_(i-1); and (5) a polypeptide backbone amide proton of amino acidresidue i, ¹H^(N) _(i). Next, radiofrequency pulses for a 5D FT NMRexperiment are applied to the sample. Then, a first set of 2 indirectchemical shift evolution periods of the 5D FT NMR experiment, ¹H^(α)_(i/i-1), and ¹³C^(α) _(i/i-1), is selected. Next, the first set of 2indirect chemical shift evolution periods is jointly sampled in a firstindirect time domain dimension, t₁(¹H^(α) _(i/i-1), ¹³C^(α) _(i/i-1)).Then, a second set of 2 indirect chemical shift evolution periods of the5D FT NMR experiment, ¹⁵N_(i) and ¹³C′_(i-1), is selected. Next, thesecond set of 2 indirect chemical shift evolution periods is jointlysampled in a second indirect time domain dimension, t₂(¹⁵N_(i),¹³C′_(i-1)). Then, NMR signals detected in a direct dimension areindependently cosine and sine modulated to generate 3D basic NMR spectracontaining frequency domain signals having a chemical shift multipletwith 4 components resulting from each of 2 chemical shift doubletcomponents in a first frequency domain dimension, ω₁(¹H^(α), ¹³C^(α)),giving rise to 2 chemical shift doublet components in a second frequencydomain dimension, ω₂(¹⁵N, ¹³C′), thereby enabling phase-sensitivesampling of all jointly sampled 4 indirect chemical shift evolutionperiods. Finally, the 3D basic NMR spectra are transformed into 3Dphase-sensitively edited basic NMR spectra, where the 4 chemical shiftmultiplet components of the 3D basic NMR spectra are edited to yield 3Dphase-sensitively edited basic NMR spectra having individual chemicalshift multiplet components. One specific embodiment of this method,(5,3)D HN{N,CO}{C ^(α) H ^(α)}, involves applying radiofrequency pulsesfor a 5D FT NMR experiment according to the scheme shown in FIG. 18.

Another aspect of the present invention relates to a method ofconducting a (5,3) dimensional (D) [{H ^(α) C ^(α)}{CON}HN] G-matrixFourier transformation (GFT) nuclear magnetic resonance (NMR)experiment. The method involves providing a sample, where the sample isa protein molecule having two consecutive amino acid residues, i−1 andi, and the chemical shift values for the following nuclei are measured:(1) α-carbon of amino acid residue i−1, ¹³C^(α) _(i-1); (2) α-proton ofamino acid residue i−1, ¹H^(α) _(i-1); (3) a polypeptide backbone amidenitrogen of amino acid residue i, ¹⁵N_(i); (4) a polypeptide backbonecarbonyl carbon of amino acid residue i−1, ¹³C′_(i-1); and (5) apolypeptide backbone amide proton of amino acid residue i, ¹H^(N) _(i).Next, radiofrequency pulses for a 5D FT NMR experiment are applied tothe sample. Then, a first set of 2 indirect chemical shift evolutionperiods of the 5D FT NMR experiment, ¹H^(α) _(i-1) and ¹³C^(α) _(i-1),is selected. Next, the first set of 2 indirect chemical shift evolutionperiods is jointly sampled in a first indirect time domain dimension,t₁(¹H^(α) _(i-1), ¹³C^(α) _(i-1)). Then, a second set of 2 indirectchemical shift evolution periods of the 5D FT NMR experiment, ¹⁵N_(i)and ¹³C′_(i-1), is selected. Next, the second set of 2 indirect chemicalshift evolution periods is jointly sampled in a second indirect timedomain dimension, t₂(¹⁵N_(i), ¹³C′_(i-1)). Then, NMR signals detected ina direct dimension are independently cosine and sine modulated togenerate 3D basic NMR spectra containing frequency domain signals havinga chemical shift multiplet with 4 components resulting from each of 2chemical shift doublet components in a first frequency domain dimension,ω₁(¹H^(α), ¹³C^(α)), giving rise to 2 chemical shift doublet componentsin a second frequency domain dimension, ω₂(¹⁵N, ¹³C′), thereby enablingphase-sensitive sampling of all jointly sampled 4 indirect chemicalshift evolution periods. Finally, the 3D basic NMR spectra aretransformed into 3D phase-sensitively edited basic NMR spectra, wherethe 4 chemical shift multiplet components of the 3D basic NMR spectraare edited to yield 3D phase-sensitively edited basic NMR spectra havingindividual chemical shift multiplet components. One specific embodimentof this method, (5,3)D {H ^(α) C ^(α)}{CON}HN, involves applyingradiofrequency pulses for a 5D FT NMR experiment according to the schemeshown in FIG. 19.

For the above six G²FT NMR experiments, the step of transforming the 3Dbasic NMR spectra into 3D phase-sensitively edited basic NMR spectra canbe carried out by applying a G-matrix defined as${{\hat{G}(1)} = {\begin{bmatrix}1 & i \\1 & {- i}\end{bmatrix} \otimes \left\lbrack {1\quad i} \right\rbrack}},$where i=√{square root over (−1)}, along the first and second indirecttime domain dimensions under conditions effective to edit the chemicalshift multiplet components in the time domain. Alternatively, thetransforming can be carried out by applying a F-matrix defined as${\hat{F}(1)} = \begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}$along the first and second frequency domain dimensions under conditionseffective to edit the chemical shift multiplet components in thefrequency domain.

Another aspect of the present invention relates to a method ofconducting a (6,3) dimensional (D) [{H ^(αβ) C ^(αβ) C ^(α)}{CON}HN]G-matrix Fourier transformation (GFT) nuclear magnetic resonance (NMR)experiment. The method involves providing a sample, where the sample isa protein molecule having two consecutive amino acid residues, i−1 andi, and the chemical shift values for the following nuclei are measured:(1) α- and β-carbons of amino acid residue i−1, ¹³C^(α/β) _(i-1); (2) α-and β-protons of amino acid residue i−1, ¹H^(α/β) _(i-1); (3) apolypeptide backbone carbonyl carbon of amino acid residue i−1,¹³C′_(i-1); (4) a polypeptide backbone amide nitrogen of amino acidresidue i, ¹⁵N_(i); and (5) a polypeptide backbone amide proton of aminoacid residue i, ¹H^(N) _(i). Next, radiofrequency pulses for a 6D FT NMRexperiment are applied to the sample. Then, a first group of 3 indirectchemical shift evolution periods of the 6D FT NMR experiment, ¹H^(α/β)_(i-1), ¹³C^(α/β) _(i-1) and ¹³C^(α) _(i-1), is selected. Next, thefirst group of 3 indirect chemical shift evolution periods is jointlysampled in a first indirect time domain dimension, t₁(¹H^(α/β) _(i-1),¹³α/β_(i-1), ¹³C^(α) _(i-1)). Then, a second group of 2 indirectchemical shift evolution periods of the 6D FT NMR experiment, ¹⁵N_(i)and ¹³C′_(i-1), is selected. Next, the second group of 2 indirectchemical shift evolution periods is jointly sampled in a second indirecttime domain dimension, t₂(¹⁵N_(i), ¹³C′_(i-1)). Then, NMR signalsdetected in a direct dimension are independently cosine and sinemodulated to generate 3D basic NMR spectra containing frequency domainsignals having a chemical shift multiplet with 8 components resultingfrom each of 4 chemical shift doublet components in a first frequencydomain dimension, Ω₁(¹³C^(α/β), ¹³C^(α)), giving rise to 2 chemicalshift doublet components in a second frequency domain dimension, ω₂(¹⁵N,¹³C′), thereby enabling phase-sensitive sampling of all jointly sampled5 indirect chemical shift evolution periods. Finally, the 3D basic NMRspectra are transformed into 3D phase-sensitively edited basic NMRspectra, where the 8 chemical shift multiplet components of the 3D basicNMR spectra are edited to yield 3D phase-sensitively edited basic NMRspectra having individual chemical shift multiplet components. Onespecific embodiment of this method, (6,3)D {H ^(αβ) C ^(αβ) C^(α)}{CON}HN, involves applying radiofrequency pulses for a 6D FT NMRexperiment according to the scheme shown in FIG. 24.

For the above (6,3)D [{H ^(αβ) C ^(αβ) C ^(α)}{CON}HN] G²FT NMRexperiment, the step of transforming the 3D basic NMR spectra into 3Dphase-sensitively edited basic NMR spectra can be carried out byapplying a G-matrix defined as ${{\hat{G}(2)} = {\begin{bmatrix}1 & i \\1 & {- i}\end{bmatrix} \otimes \begin{bmatrix}1 & i \\1 & {- i}\end{bmatrix} \otimes \left\lbrack {1\quad i} \right\rbrack}},$where i=√{square root over (−1)}, along the first indirect time domaindimension and applying a G-matrix defined as${\hat{G}(1)} = {\begin{bmatrix}1 & i \\1 & {- i}\end{bmatrix} \otimes \left\lbrack {1\quad i} \right\rbrack}$along the second indirect time domain dimension under conditionseffective to edit the chemical shift multiplet components in the timedomain. Alternatively, the transforming can be carried out by applying aF-matrix defined as {circumflex over (F)}(2)={circumflex over(F)}(1){circle around (×)}{circumflex over (F)}(1), where${{\hat{F}(1)} = \begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}},$along the first frequency domain dimension and applying a F-matrixdefined as ${\hat{F}(1)} = \begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}$along the second frequency domain dimension under conditions effectiveto edit the chemical shift multiplet components in the frequency domain.

With the information of ¹H^(αβ) and ¹³C^(α/β) chemical shifts obtainedin the above G²FT NMR experiments, a (5,3)D [HC(C)C—CH] GFT NMRexperiment can be conducted to assign the more peripheral spins of thealiphatic side chain of a given amino acid residue, where the hyphenrepresents the fact that ¹³C^(coupled) is frequency labeled twice while,for nuclei in parentheses, chemical shift evolution is omitted.

Thus, yet another aspect of the present invention relates to a method ofconducting a (5,3) dimensional (D) [HC(C)C—CH] G-matrix Fouriertransformation (GFT) nuclear magnetic resonance (NMR) experiment. Themethod involves providing a sample, where the sample is a proteinmolecule and the chemical shift values for the following nuclei aremeasured: (1) a proton, ¹H; (2) a carbon coupled to ¹H, ¹³C; (3) acarbon coupled, via another carbon, to ¹³C, ¹³C^(coupled); and (4) aproton coupled to ¹³C^(coupled), ¹H^(coupled), where the chemical shiftof ¹³C^(coupled) provides signal dispersion in an indirect dimension.Next, radiofrequency pulses for a 5D FT NMR experiment are applied tothe sample. Then, 3 indirect chemical shift evolution periods of the 5DFT NMR experiment, ¹H, ¹³C, and ¹³C^(coupled), are selected. Next, the 3indirect chemical shift evolution periods are jointly sampled in anindirect time domain dimension, t₁(¹H,¹³C,¹³C^(coupled)). Then, NMRsignals detected in a direct dimension are independently cosine and sinemodulated to generate 3D basic NMR spectra containing frequency domainsignals with 4 chemical shift multiplet components, thereby enablingphase-sensitive sampling of all jointly sampled 3 indirect chemicalshift evolution periods. Finally, the 3D basic NMR spectra aretransformed into 3D phase-sensitively edited basic NMR spectra, wherethe 4 chemical shift multiplet components of the 3D basic NMR spectraare edited to yield 3D phase-sensitively edited basic NMR spectra havingindividual chemical shift multiplet components. One specific embodimentof this method, (5,3)D HC(C)C—CH, involves applying radiofrequencypulses for a 5D FT NMR experiment according to the scheme shown in FIG.27.

In another embodiment, the method of conducting a (5,3)D [HC(C)C—CH] GFTNMR experiment can further involve repeating once the steps of jointlysampling, independently cosine and sine modulating, and transforming,where the jointly sampling involves jointly sampling 2 indirect chemicalshift evolution periods out of the 3 indirect chemical shift evolutionperiods, under conditions effective to generate a first order centralpeak NMR spectrum.

In another embodiment for the above method of conducting a (5,3)D[HC(C)C—CH] GFT NMR experiment, the step of transforming the 3D basicNMR spectra into 3D phase-sensitively edited basic NMR spectra can becarried out by applying a G-matrix defined as${{\hat{G}(2)} = {\begin{bmatrix}1 & i \\1 & {- i}\end{bmatrix} \otimes \begin{bmatrix}1 & i \\1 & {- i}\end{bmatrix} \otimes \left\lbrack {1i} \right\rbrack}},$where i=√{square root over (−1)}, under conditions effective to edit thechemical shift multiplet components in a time domain. Alternatively, thetransforming can be carried out by applying a F-matrix defined as{circumflex over (F)}(2)={circumflex over (F)}(1){circle around(×)}{circumflex over (F)}(1), where ${{\hat{F}(1)} = \begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}},$under conditions effective to edit the chemical shift multipletcomponents in a frequency domain.L-GFT NMR of Proteins with Aromatic Rings

The present application discloses aromatic L-GFT and L-GFT-TROSY (4,3)D[HCCH] (as well as (4,3)D [HCCH] and (4,3)D [HCCH]). Sensitivity ismaximized by using (i) newly introduced longitudinal relaxation(L-)optimization (Pervushin et al., J. Am. Chem. Soc. 124:12898-12902(2002), which is hereby incorporated by reference in its entirety) foraromatic protons (¹H^(aromatic)), (ii) pulsed field gradient (PFG)selection of coherences with preservation of equivalent pathways (PEP)(Cavanagh et al., Protein NMR Spectroscopy: Principles and PracticeAcademic Press: San Diego (1996); Kay et al., J. Am. Chem. Soc.114:10663-10665 (1992), which are hereby incorporated by reference intheir entirety), (iii) (semi-) constant time (ct) frequency labeling(Cavanagh et al., Protein NMR Spectroscopy: Principles and PracticeAcademic Press: San Diego (1996), which is hereby incorporated byreference in its entirety), and (iv) employment of transverse relaxationoptimized spectroscopy (TROSY; Pervushin et al., Proc. Natl. Acad. Sci.USA 94:12366-12371 (1997); Pervushin et al., J. Am. Chem. Soc.120:6394-6400 (1998); Meissner et al., J. Magn. Reson. 139:447-450(1999), which are hereby incorporated by reference in their entirety).Rapid sampling is accomplished by use of G-matrix FT (GFT) NMR (Kim etal., J. Am. Chem. Soc. 125:1385-1393 (2003), which is herebyincorporated by reference in its entirety) combined (Atreya et al.,Proc. Natl. Acad. Sci. USA 101:9642-9647 (2004); Atreya et al., MethodEnzymol. 394:78-108 (2005), which are hereby incorporated by referencein their entirety) with L-optimization, which thus serves to enhancesensitivity (Pervushin et al., J. Am. Chem. Soc. 124:12898-12902 (2002),which is hereby incorporated by reference in its entirety) and/orshorten relaxation delays (Atreya et al., Proc. Natl. Acad. Sci. USA101:9642-9647 (2004), which is hereby incorporated by reference in itsentirety). ¹H^(aromatic) L-optimization is feasible since (i)¹H^(aromatic)/¹H₂O and ¹H^(aliphatic) chemical shift ranges do notoverlap, which enables selective “flipping” of ¹H^(aliphatic)/¹H₂Omagnetization while ¹H^(aromatic) magnetization is along z, and (ii) alarge number of dipolar ¹H^(aromatic)—¹H^(aliphatic) and Tyr¹H^(aromatic)—¹H^(hydroxyl) interactions can increase R₁ of¹H^(aromatic).

Thus, the present invention relates to a method of conducting alongitudinal aromatic proton relaxation optimized (4,3) dimensional (D)[HCCH] G-matrix Fourier transformation (GFT) nuclear magnetic resonance(NMR) experiment. The method involves providing a sample, where thesample is a protein molecule and the chemical shift values for thefollowing nuclei are measured: (1) an aromatic proton, ¹H; (2) anaromatic carbon coupled to ¹H, ¹³C; (3) a carbon coupled to ¹³C,¹³C^(coupled); and (4) a proton coupled to ¹³C^(coupled), ¹H^(coupled).Next, radiofrequency pulses for a 4D FT NMR experiment are applied tothe sample, under conditions effective to allow longitudinal relaxationoptimization of the aromatic protons. Then, 2 indirect chemical shiftevolution periods of the 4D FT NMR experiment, ¹H and ¹³C, are selected.Next, the 2 indirect chemical shift evolution periods are jointlysampled in an indirect time domain dimension, t₁(¹H, ¹³C). Then, NMRsignals detected in a direct dimension are independently cosine and sinemodulated to generate 3D basic NMR spectra containing frequency domainsignals with 2 chemical shift doublet components, thereby enablingphase-sensitive sampling of the jointly sampled 2 indirect chemicalshift evolution periods. Finally, the 3D basic NMR spectra aretransformed into 3D phase-sensitively edited basic NMR spectra, wherethe 2 chemical shift doublet components of the 3D basic NMR spectra areedited to yield 3D phase-sensitively edited basic NMR spectra havingindividual chemical shift doublet components. One specific embodiment ofthis method, (4,3)D HCCH, involves applying radiofrequency pulses for a4D FT NMR experiment according to the scheme shown in FIG. 32.

Another aspect of the present invention relates to a method ofconducting a longitudinal aromatic proton relaxation optimized (4,3)dimensional (D) [HCCH] G-matrix Fourier transformation (GFT) nuclearmagnetic resonance (NMR) experiment. The method involves providing asample, where the sample is a protein molecule and the chemical shiftvalues for the following nuclei are measured: (1) an aromatic proton,¹H; (2) an aromatic carbon coupled to ¹H, ¹³C; (3) a carbon coupled to¹³C, ¹³C^(coupled); and (4) a proton coupled to ¹³C^(coupled),¹H^(coupled). Next, radiofrequency pulses for a 4D FT NMR experiment areapplied to the sample under conditions effective to allow longitudinalrelaxation optimization of the aromatic protons. Then, 2 indirectchemical shift evolution periods of the 4D FT NMR experiment, ¹³C and¹³C^(coupled), are selected. Next, the 2 indirect chemical shiftevolution periods are jointly sampled in an indirect time domaindimension, t₁(¹³C, ¹³C^(coupled)). Then, NMR signals detected in adirect dimension are independently cosine and sine modulated to generate3D basic NMR spectra containing frequency domain signals with 2 chemicalshift doublet components, thereby enabling phase-sensitive sampling ofthe jointly sampled 2 indirect chemical shift evolution periods.Finally, the 3D basic NMR spectra are transformed into 3Dphase-sensitively edited basic NMR spectra, where the 2 chemical shiftdoublet components of the 3D basic NMR spectra are edited to yield 3Dphase-sensitively edited basic NMR spectra having individual chemicalshift doublet components.

Another aspect of the present invention relates to a method ofconducting a longitudinal aromatic proton relaxation optimized (4,3)dimensional (D) [HCCH] G-matrix Fourier transformation (GFT) nuclearmagnetic resonance (NMR) experiment. The method involves providing asample, where the sample is a protein molecule and the chemical shiftvalues for the following nuclei are measured: (1) an aromatic proton,¹H; (2) an aromatic carbon coupled to ¹H, ¹³C; (3) a carbon coupled to¹³C, ¹³C^(coupled); and (4) a proton coupled to ¹³C^(coupled),¹H^(coupled). Next, radiofrequency pulses for a 4D FT NMR experiment areapplied to the sample under conditions effective to allow longitudinalrelaxation optimization of the aromatic protons. Then, 2 indirectchemical shift evolution periods of the 4D FT NMR experiment, ¹H and¹³C^(coupled), are selected. Next, the 2 indirect chemical shiftevolution periods are jointly sampled in an indirect time domaindimension, t₁(¹H, ¹³C^(coupled)). Then, NMR signals detected in a directdimension are independently cosine and sine modulated to generate 3Dbasic NMR spectra containing frequency domain signals with 2 chemicalshift doublet components, thereby enabling phase-sensitive sampling ofthe jointly sampled 2 indirect chemical shift evolution periods.Finally, the 3D basic NMR spectra are transformed into 3Dphase-sensitively edited basic NMR spectra, where the 2 chemical shiftdoublet components of the 3D basic NMR spectra are edited to yield 3Dphase-sensitively edited basic NMR spectra having individual chemicalshift doublet components.

For the above three L-GFT (4,3)D NMR experiments, the step oftransforming the 3D basic NMR spectra into 3D phase-sensitively editedbasic NMR spectra can be carried out by applying a G-matrix defined as${{\hat{G}(1)} = {\begin{bmatrix}1 & i \\1 & {- i}\end{bmatrix} \otimes \left\lbrack {1i} \right\rbrack}},$where i=√{square root over (−1)}, under conditions effective to edit thechemical shift doublet components in a time domain. Alternatively, thetransforming can be carried out by applying a F-matrix defined as${{\hat{F}(1)} = \begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}},$under conditions effective to edit the chemical shift doublet componentsin a frequency domain.GFT NOESY NMR Experiments

The present application discloses a through-bond GFT NMR based resonanceassignment protocol (Atreya et al., Proc. Natl. Acad. Sci. USA101:9642-9647 (2004); Kim et al., J. Am. Chem. Soc. 125:1385-1393(2003); Kim et al., J. Biomol. NMR 28:117-130 (2004), which are herebyincorporated by reference in their entirety) used in conjunction with anewly implemented NOESY experiment combining simultaneous (Farmer etal., J. Biomol. NMR 4:673-687 (1994); Pascal et al., J. Magn. Reson.103:197-201 (1994); Jerala et al., J. Magn. Reson. B108:294-298 (1995);Uhrin et al., J. Biomol. NMR 18:253-259 (2000); Xia et al., J. Biomol.NMR 27:193-203 (2003), which are hereby incorporated by reference intheir entirety) and GFT (Atreya et al., Proc. Natl. Acad. Sci. USA101:9642-9647 (2004); Kim et al., J. Am. Chem. Soc. 125:1385-1393(2003); Kim et al., J. Biomol. NMR 28:117-130 (2004), which are herebyincorporated by reference in their entirety) NMR data acquisition. Oneof the experiments is named “GFT (4,3)D [HC^(ali)/HN]-NOESY-[CH^(ali)/NH]”, where the underlined letters denotenuclei for which the shifts are jointly sampled. The NOESY experimentencodes in two subspectra, the information of 4D ¹⁵N/¹⁵N-,¹³C^(alipahtic)/¹⁵N-, and ¹³C^(aliphatic)/¹³C^(aliphatic)-resolved[¹H,¹H]-NOESY. Each of the subspectra contain one component of achemical shift doublet manifested along the GFT dimension atω₁:Ω(¹H)±Ω(X) [X=¹⁵N, ¹³C^(aliphatic)]. A third subspectrum, containingpeaks located at the centers of the shift doublets at ω₁:Ω(¹H), encodesthe information of 3D ¹⁵N- and ¹³C^(aliphatic)-resolved [¹H,¹H]-NOESY.Preferably, central peaks are recorded in simultaneous 3D¹⁵N/¹³C^(aliphatic)/¹³C^(aromatic)-resolved [¹H,¹H]-NOESY (named herefor brevity 3D [H]-NOESY-[CH^(ali)/CH^(aro)/NH]); this allows one todetect NOEs on aromatic protons along with the desired central peaks.

The impact of the simultaneous GFT NOESY data collection strategy isdescribed herein in detail, since it is a priori not straightforward toidentify sampling-limited (Szyperski et al., Proc. Natl. Acad. Sci. USA.99:8009-8014 (2002), which is hereby incorporated by reference in itsentirety) NOESY data acquisition. Longer measurement times and theresulting increased S/N ratios lead to detection of additional NOEscorresponding to longer ¹H—¹H distances. This may have significantimpact on the precision of the final NMR structure, and the soleanalysis of S/N ratio distributions (for example, of intraresidue andsequential NOEs) is not sufficient. Hence, one has to assess for (4,3)DNOESY: (i) the relative sensitivity of chemical shift doublet versuscentral peak detection, (ii) the increase in the fraction of centralpeak NOEs that can be assigned directly based on chemical shift datawhen having the additional information encoded in shift doublets, (iii)its impact on precision and accuracy of initial NMR structures obtainedbased on chemical shift data only, (iv) its value relative tocomputational techniques for generating initial structures from centralpeaks detected in 3D NOESY without reference to an initial structure,and (v) the number of additionally resolved and assigned NOEs allowingone to obtain a well-refined NMR structure. These criteria are centralfor establishing the role of (4,3)D [HC ^(ali)/HN]-NOESY-[CH^(ali)/NH]for efficient NOE-based structure determination.

Thus, the present invention relates to a method of conducting a (3,2)dimensional (D) <[¹ H ^(X) X]-nuclear Overhauser enhancementspectroscopy (NOESY)-[¹H]> G-matrix Fourier transformation (GFT) nuclearmagnetic resonance (NMR) experiment. The method involves providing asample, where the sample is a protein molecule and the chemical shiftvalues for the following nuclei are measured: (1) a proton, ¹H; (2) X,wherein X is an aliphatic carbon, ¹³C^(ali), an aromatic carbon,¹³C^(aro), or a nitrogen, ¹⁵N; and (3) a proton bound to X, 1H^(X).Next, radiofrequency pulses for a first 3D NOESY FT NMR experiment areapplied to the sample. Then, a first set of 2 indirect chemical shiftevolution periods of the 3D NOESY FT NMR experiment, ¹H^(X) and X, isjointly sampled in an indirect time domain dimension, t₁(¹H^(X),X).Next, NMR signals detected in a direct dimension are independentlycosine and sine modulated to generate 2D basic NMR spectra containingfrequency domain signals with 2 chemical shift doublet components,thereby enabling phase-sensitive sampling of the jointly sampled firstset of 2 indirect chemical shift evolution periods. Finally, the 2Dbasic NMR spectra are transformed into 2D phase-sensitively edited basicNMR spectra, where the 2 chemical shift doublet components of the 2Dbasic NMR spectra are edited to yield 2D phase-sensitively edited basicNMR spectra having individual chemical shift doublet components.

In another embodiment, the above method involves further measuringchemical shift values for the following nuclei to conduct a (3,2)D <[¹ H^(X) X/¹ H ^(Y) Y]-NOESY-[¹H]> GFT NMR experiment: (1) Y, where Y is analiphatic carbon, ¹³C^(ali), an aromatic carbon, ¹³C^(aro), or anitrogen, ¹⁵N, and (2) ¹H^(Y), a proton bound to Y, where (a) the stepof applying further involves simultaneously applying radiofrequencypulses for a second 3D NOESY FT NMR experiment to the sample, (b) thestep of jointly sampling further involves simultaneously jointlysampling a second set of 2 indirect chemical shift evolution periods ofthe 3D NOESY FT NMR experiment, ¹H^(Y) and Y, and (c) the step ofindependently cosine and sine modulating further involves simultaneousphase-sensitive sampling of the jointly sampled second set of indirectchemical shift evolution periods.

In another embodiment, the above method involves further measuringchemical shift values for the following nuclei to conduct a (3,2)D <[¹ H^(X) X/¹ H ^(Y) Y/¹ H ^(Z) Z]-NOESY-[¹H]> GFT NMR experiment: (1) Z,where Z is an aliphatic carbon, ¹³C^(ali), an aromatic carbon,I³C^(aro), or a nitrogen, ¹⁵N, and (2) ¹H^(Z), a proton bound to Z,where (a) the step of applying further involves simultaneously applyingradiofrequency pulses for a third 3D NOESY FT NMR experiment to thesample, (b) the step of jointly sampling further involves simultaneouslyjointly sampling a third set of 2 indirect chemical shift evolutionperiods of the 3D NOESY FT NMR experiment, ¹H^(Z) and Z, and (c) thestep of independently cosine and sine modulating further involvessimultaneous phase-sensitive sampling of the jointly sampled third setof indirect chemical shift evolution periods. One specific embodiment ofthis method, (3,2)D [¹ H ^(X) X/¹ H ^(Y) Y/¹ H ^(Z) Z]-NOESY-[¹H],involves applying radiofrequency pulses for a 4D FT NMR experimentaccording to the scheme shown in FIG. 46.

Another aspect of the present invention relates to a method ofconducting a (4,3) dimensional (D) <[1HXX]-nuclear Overhauserenhancement spectroscopy (NOESY)-[Y¹H^(Y)]> G-matrix Fouriertransformation (GFT) nuclear magnetic resonance (NMR) experiment. Themethod involves providing a sample, where the sample is a proteinmolecule and the chemical shift values for the following nuclei aremeasured: (1) X, wherein X is an aliphatic carbon, ¹³C^(ali), anaromatic carbon, ¹³C^(aro), or a nitrogen, ¹⁵N; (2) a proton bound to X,¹H^(X); (3) Y, wherein Y is an aliphatic carbon, ¹³C^(ali), an aromaticcarbon, ¹³C^(aro), or a nitrogen, ¹⁵N; and (4) a proton bound to Y,¹H^(Y). Next, radiofrequency pulses for a first 4D NOESY FT NMRexperiment are applied to the sample. Then, a first set of 2 indirectchemical shift evolution periods of the 4D NOESY FT NMR experiment,¹H^(X) and X, is selected. Next, the first set of 2 indirect chemicalshift evolution periods is jointly sampled in an indirect time domaindimension, t₁(¹H^(X),X). Then, NMR signals detected in a directdimension are independently cosine and sine modulated to generate 3Dbasic NMR spectra containing frequency domain signals with 2 chemicalshift doublet components, thereby enabling phase-sensitive sampling ofthe jointly sampled 2 indirect chemical shift evolution periods.Finally, the 3D basic NMR spectra are transformed into 3Dphase-sensitively edited basic NMR spectra, where the 2 chemical shiftdoublet components of the 3D basic NMR spectra are edited to yield 3Dphase-sensitively edited basic NMR spectra having individual chemicalshift doublet components.

In another embodiment, the above method involves further measuringchemical shift values for the following nuclei to conduct a (4,3)D <[¹ H^(X) X/¹ H ^(X′) X′]-NOESY-[Y¹H^(Y)/Y′¹H^(Y′)]> GFT NMR experiment: (1)X′, where X′ is an aliphatic carbon, ¹³C^(ali), an aromatic carbon,¹³C^(aro), or a nitrogen, ¹⁵N; (2) a proton bound to X′, ¹H^(X′); (3)Y′, where Y′ is an aliphatic carbon, ¹³C^(ali), an aromatic carbon,¹³C^(aro), or a nitrogen, ¹⁵N; and (4) a proton bound to Y′, ¹H^(Y′),where (a) the step of applying further involves simultaneously applyingradiofrequency pulses for a second 4D NOESY FT NMR experiment to thesample, (b) the step of jointly sampling further involves simultaneouslyjointly sampling a second set of 2 indirect chemical shift evolutionperiods of the 4D NOESY FT NMR experiment, ¹H^(Y) and Y, and (c) thestep of independently cosine and sine modulating further involvessimultaneous phase-sensitive sampling of the jointly sampled second setof indirect chemical shift evolution periods. One specific embodiment ofthis method, (4,3)D [¹ H ^(X) X/¹ H ^(X′) X′]-NOESY-[Y¹H^(Y)/Y′¹H^(Y′)],involves applying radiofrequency pulses for a simultaneous 4D NOESY FTNMR experiment according to the scheme shown in FIG. 36(a).

For the above GFT NOESY NMR experiments, the step of transforming the 3Dbasic NMR spectra into 3D phase-sensitively edited basic NMR spectra canbe carried out by applying a G-matrix defined as${{\hat{G}(1)} = {\begin{bmatrix}1 & i \\1 & {- i}\end{bmatrix} \otimes \left\lbrack {1i} \right\rbrack}},$where i=√{square root over (−1)}, under conditions effective to edit thechemical shift doublet components in a time domain. Alternatively, thetransforming can be carried out by applying a F-matrix defined as${{\hat{G}(1)} = {\begin{bmatrix}1 & i \\1 & {- i}\end{bmatrix} \otimes \left\lbrack {1i} \right\rbrack}},$under conditions effective to edit the chemical shift doublet componentsin a frequency domain.

Another aspect of the present invention relates to a method ofconducting a (4,2) dimensional (D) <[¹ H ^(X) X]-nuclear Overhauserenhancement spectroscopy (NOESY)-[Y ¹H^(Y)]> G-matrix Fouriertransformation (GFT) nuclear magnetic resonance (NMR) experiment. Themethod involves providing a sample, where the sample is a proteinmolecule and the chemical shift values for the following nuclei aremeasured: (1) X, where X is an aliphatic carbon, ¹³C^(ali), an aromaticcarbon, ¹³C^(aro), or a nitrogen, ¹⁵N; (2) a proton bound to X, ¹H^(X);(3) Y, where Y is an aliphatic carbon, ¹³C^(ali), an aromatic carbon,¹³C^(aro), or a nitrogen, ¹⁵N; and (4) a proton bound to Y, ¹H^(Y).Next, radiofrequency pulses for a first 4D NOESY FT NMR experiment areapplied to the sample. Then, a first group of 3 indirect chemical shiftevolution periods of the 4D NOESY FT NMR experiment, ¹H^(X), X, and Y,is selected. Next, the first group of 3 indirect chemical shiftevolution periods is jointly sampled in an indirect time domaindimension, t₁(¹H^(X),X,Y). Then, NMR signals detected in a directdimension are independently cosine and sine modulated to generate 2Dbasic NMR spectra containing frequency domain signals with 4 chemicalshift multiplet components, thereby enabling phase-sensitive sampling ofall jointly sampled 3 indirect chemical shift evolution periods.Finally, the 2D basic NMR spectra are transformed into 2Dphase-sensitively edited basic NMR spectra, where the 4 chemical shiftmultiplet components of the 2D basic NMR spectra are edited to yield 2Dphase-sensitively edited basic NMR spectra having individual chemicalshift multiplet components. One specific embodiment of this method,(4,2)D [¹ H ^(X) X]-NOESY-[Y ¹H^(Y)], involves applying radiofrequencypulses for a simultaneous 4D NOESY FT NMR experiment according to thescheme shown in FIG. 44.

In another embodiment, the above method involves further measuringchemical shift values for the following nuclei to conduct a (4,2)D <[¹ H^(X) X/¹ H ^(X′) X′]-NOESY-[Y ¹H^(Y)/Y′ ¹H^(Y′)]> GFT NMR experiment:(1) X′, where X′ is an aliphatic carbon, ¹³C^(ali), an aromatic carbon,13Caro, or a nitrogen, ¹⁵N; (2) a proton bound to X′, ¹H^(X′); (3) Y′,where Y′ is an aliphatic carbon, ¹³C^(ali), an aromatic carbon,¹³C^(aro), or a nitrogen, ¹⁵N; and (4) a proton bound to Y′, ¹H^(Y′),where (a) the step of applying further involves simultaneously applyingradiofrequency pulses for a second 4D NOESY FT NMR experiment to thesample, (b) the step of jointly sampling further involves simultaneouslyjointly sampling a second group of 3 indirect chemical shift evolutionperiods of the 4D NOESY FT NMR experiment, ¹H^(X′), X′, and Y′, and (c)the step of independently cosine and sine modulating further involvessimultaneous phase-sensitive sampling of the jointly sampled secondgroup of indirect chemical shift evolution periods.

For the above GFT NOESY NMR experiments, the step of transforming the 3Dbasic NMR spectra into 3D phase-sensitively edited basic NMR spectra canbe carried out by applying a G-matrix defined as${{\hat{G}(2)} = {\begin{bmatrix}1 & i \\1 & {- i}\end{bmatrix} \otimes \begin{bmatrix}1 & i \\1 & {- i}\end{bmatrix} \otimes \left\lbrack {1i} \right\rbrack}},$where i=√{square root over (−1)}, under conditions effective to edit thechemical shift multiplet components in a time domain. Alternatively, thetransforming can be carried out by applying a F-matrix defined as{circumflex over (F)}(2)={circumflex over (F)}(1){circle around(×)}{circumflex over (F)}(1), wherein ${{\hat{F}(1)} = \begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}},$under conditions effective to edit the chemical shift multipletcomponents in a frequency domain.

In another embodiment, the above methods further involve repeating oncethe step of jointly sampling, independently cosine and sine modulating,and transforming, where the step of jointly sampling involves jointlysampling 2 indirect chemical shift evolution periods out of the 3indirect chemical shift evolution periods, under conditions effective togenerate a first order central peak NMR spectrum.

J-GFT NMR Experiments

The present application discloses a constant-time (ct) G-matrix Fouriertransform (GFT) NMR experiment (Kim et al., J. Am. Chem. Soc.125:1385-1393 (2003), which is hereby incorporated by reference in itsentirety), which circumvents the drawbacks aforementioned in theBackground of the Invention section for simultaneous and precisemeasurement of multiple correlated RDCs in proteins. GFT NMR has beenpreviously shown to yield highly precise multi-dimensional spectralinformation rapidly for protein resonance assignments (Kim et al., J.Am. Chem. Soc. 125:1385-1393 (2003); Atreya et al., Proc. Natl. Acad.Sci. USA 101:9642-9647 (2004); Kim et al., J. Biomol. NMR 28:117-130(2004); Atreya et al., J. Am. Chem. Soc. 127:4554-4555 (2005); Shen etal., J. Am. Chem. Soc. 127:9085-9099 (2005), which are herebyincorporated by reference in their entirety) by phase sensitive jointchemical shift sampling of several nuclei in a single indirect dimensioncalled the GFT-dimension (Kim et al., J. Am. Chem. Soc. 125:1385-1393(2003); Atreya et al., Proc. Natl. Acad. Sci. USA 101:9642-9647 (2004),which are hereby incorporated by reference in their entirety). Such ascheme is employed in the present invention for simultaneous measurementof several scalar and dipolar couplings in proteins. Four mutuallycorrelated one-bond couplings, namely, ¹³C^(α)—¹H^(α)(¹J_(C)α_(H)α/¹D_(C)α_(H)α), ¹³C^(α)—¹³C′ (¹J_(C)α_(C′)/¹D_(C)α_(C′)),¹⁵N—¹³C′ (¹J_(NC′)/¹D_(NC′)), and ¹⁵N—¹H^(N) (¹J_(NH)/¹D_(NH)) aresimultaneously measured in conjunction with ¹⁵N and ¹H^(N) chemicalshifts. The novel experiment is named “J-GFT (6,2)D[(H^(α)—C^(α)—CO)—N—HN]”, where each hyphen represents one of themeasured (scalar/residual dipolar) one-bond couplings while, for nucleiin parentheses, chemical shift evolution is omitted.

Thus, the present invention also relates to a method of conducting a(6,2) dimensional (D) [(H^(α)—C^(α)—CO)—N—HN] G-matrix Fouriertransformation (GFT) nuclear magnetic resonance (NMR) experiment. Themethod involves providing a sample, where the sample is a proteinmolecule having two consecutive amino acid residues, i−1 and i, and thechemical shift values for the following nuclei: (1) a polypeptidebackbone amide nitrogen of amino acid residue i, ¹⁵N_(i); and (2) apolypeptide backbone amide proton of amino acid residue i, ¹H^(N) _(i),are measured in combination with four spin-spin couplings between (1) anα-proton of amino acid residue i−1, ¹H^(α) _(i-1), and an α-carbon ofamino acid residue i−1, ¹³C^(α) _(i-1); (2) an α-carbon of amino acidresidue i−1, ¹³C^(α) _(i-1), and a polypeptide backbone carbonyl carbonof amino acid residue i−1, ¹³C′_(i-1); (3) a polypeptide backbonecarbonyl carbon of amino acid residue i−1, ¹³C′_(i-1), and a polypeptidebackbone amide nitrogen of amino acid residue i, ¹⁵N_(i); (4) apolypeptide backbone amide nitrogen of amino acid residue i, ¹⁵N_(i),and a polypeptide backbone amide proton of amino acid residue i, ¹H^(N)_(i). Next, radiofrequency pulses for a 6D FT NMR experiment are appliedto the sample. Then, an indirect chemical shift evolution period of the6D FT NMR experiment, ¹⁵N_(i), is selected. Next, the indirect chemicalshift evolution period is jointly sampled with four indirect spin-spincoupling evolution periods resulting from sampling the four spin-spincouplings. Then, NMR signals detected in a direct dimension resultingfrom time evolution of the indirect chemical shift and the fourspin-spin couplings are independently cosine and sine modulated togenerate 2D basic NMR spectra containing frequency domain signals with16 multiplet components, thereby enabling phase-sensitive sampling ofthe indirect chemical shift evolution period and the indirect spin-spincoupling evolution periods. Finally, the 2D basic NMR spectra aretransformed into 2D phase-sensitively edited basic NMR spectra, wherethe 16 multiplet components of the 2D basic NMR spectra are edited toyield 2D phase-sensitively edited basic NMR spectra having individualmultiplet components. One specific embodiment of this method, (6,2)D(H^(α)—C^(α)—CO)—N—HN, involves applying radiofrequency pulses for a 6DFT NMR experiment according to the scheme shown in FIG. 47.

For the above J-GFT NMR experiments, the step of transforming the 2Dbasic NMR spectra into 2D phase-sensitively edited basic NMR spectra canbe carried out by applying a G-matrix defined as${{\hat{G}(4)} = {\begin{bmatrix}1 & i \\1 & {- i}\end{bmatrix} \otimes \begin{bmatrix}1 & i \\1 & {- i}\end{bmatrix} \otimes \begin{bmatrix}1 & i \\1 & {- i}\end{bmatrix} \otimes \begin{bmatrix}1 & i \\1 & {- i}\end{bmatrix} \otimes \left\lbrack {1i} \right\rbrack}},$where i=√{square root over (−1)}, under conditions effective to edit themultiplet components in a time domain. Alternatively, the transformingcan be carried out by applying a F-matrix defined as {circumflex over(F)}(4)={circumflex over (F)}(1){circle around (×)}{circumflex over(F)}(1){circle around (×)}{circumflex over (F)}(1){circle around(×)}{circumflex over (F)}(1), wherein ${{\hat{F}(1)} = \begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}},$under conditions effective to edit the multiplet components in afrequency domain.

In addition, a further aspect of the present invention relates toconducting other (6,2)D GFT NMR experiments (e.g., (6,2)D[H^(α)—(C^(α)—CO—N)—HN], (6,2)D [H^(α)—C^(α)—(CO—N—HN)], etc.), wherechemical shift values for different selections of 2 nuclei (e.g.,¹³H^(α) _(i-1) and ¹H^(N) _(i), ¹³H^(α) _(i-1) and ¹³C^(α) _(i-1), etc.)are measured in combination with the four spin-spin couplings.

Another aspect of the present invention relates to conducting (7,2)D GFTNMR experiments (e.g., (7,2)D [(H^(α)—C^(α))—CO—N—HN], (7,2)D[H^(α)—(C^(α)—CO)—N—HN], (7,2)D [H^(α)—C^(α)—(CO—N)—HN], (7,2)D[H^(α)—C^(α)—CO—(N—HN)], etc.), where chemical shift values for anyselection of 3 nuclei (e.g., ¹³C′_(i-1), ¹⁵N_(i), and ¹H^(N) _(i);¹³H^(α) _(i-1), ¹⁵N_(i), and ¹H^(N) _(i); ¹³H^(α) _(i-1), ¹³C^(α)_(i-1), and ¹H^(N) _(i); ¹³H^(α) _(i-1), ¹³C^(α) _(i-1), and ¹³C′_(i-1),etc.) are measured in combination with the four spin-spin couplings.

Another aspect of the present invention relates to conducting (8,2)D GFTNMR experiments (e.g., (8,2)D [(H^(α))—C^(α)—CO—N—HN], (8,2)D[H^(α)—(C^(α))—CO—N—HN], (8,2)D [H^(α)—C^(α)—CO—(N)—HN], (8,2)D[H^(α)—C^(α)—CO—N—(HN)], etc.), where chemical shift values for anyselection of 4 nuclei (e.g., ¹³C^(α) _(i-1), ¹³C′_(i-1), ¹⁵N_(i), and¹H^(N) _(i); ¹³H^(α) _(i-1), ¹³C′_(i-1), ¹⁵N_(i), and ¹H^(N) _(i);¹³H^(α) _(i-1), ¹³C^(α) _(i-1), ¹³C′_(i-1), and ¹H^(N) _(i); ¹³H^(α)_(i-1), ¹³C^(α) _(i-1), ¹³C′_(i-1), and ¹H^(N) _(i), etc.) are measuredin combination with the four spin-spin couplings.

Another aspect of the present invention relates to conducting a (9,2)DGFT NMR experiment (i.e., (9,2)D [H^(α)—C^(α)—CO—N—HN]), where chemicalshift values for all 5 nuclei (i.e., ¹³H^(α) _(i-1), ¹³C^(α) _(i-1),¹³C′_(i-1), ¹⁵N_(i), and ¹H^(N) _(i)) are measured in combination withthe four spin-spin couplings.

In addition, the present invention relates to conducting (5,2)D GFT NMRexperiments (e.g., (5,2)D [(H^(α)C^(α)—CO)—N—HN], (5,2)D[(H^(α)—C^(α)CO)—N—HN], (5,2)D [(H^(α)—C^(α)—CO)N—HN], etc.), wherechemical shift values for any selection of the nuclei are measured incombination with 3 spin-spin couplings (e.g., between ¹³C^(α) _(i-1) and¹³C′_(i-1), ¹³C′_(i-1) and ¹⁵N_(i), and ¹⁵N_(i) and ¹H^(N) _(i); between¹³H^(α) _(i-1) and ¹³C^(α) _(i-1), ¹³C′_(i-1) and ¹⁵N_(i), and ¹⁵N_(i)and ¹H^(N) _(i); between ¹³H^(α) _(i-1) and ¹³C^(α) _(i-1), ¹³C^(α)_(i-1) and ¹³C′_(i-1), and ¹⁵N_(i) and ¹H^(N) _(i), etc.).

In addition, the present invention relates to conducting (4,2)D GFT NMRexperiments (e.g., (4,2)D [(H^(α)C^(α)CO)—N—HN], (4,2)D[(H^(α)—C^(α)CO)N—HN], (4,2)D [(H^(α)—C^(α)—CO)NHN], etc.), wherechemical shift values for any selection of the nuclei are measured incombination with 2 spin-spin couplings (e.g., between ¹³C′_(i-1) and¹⁵N_(i), and ¹⁵N_(i) and ¹H^(N) _(i); between ¹³H^(α) _(i-1) and ¹³C^(α)_(i-1), and ¹⁵N_(i) and ¹H^(N) _(i); between ¹³H^(α) _(i-1) and ¹³C^(α)_(i-1), and ¹³C^(α) _(i-1) and ¹³C′_(i-1), etc.).

EXAMPLES

The following examples are provided to illustrate embodiments of thepresent invention but are by no means intended to limit its scope.

Example 1 G²F (5,3)D HN{N,CO}{C ^(αβ) C ^(α)} and G²FT (5,3)D HN{NCO}{C^(αβ) C ^(α)}/(5,3)D {C ^(αβ) C ^(α)}{CON}HN NMR Experiments

NMR assignments of proteins are obtained by combining severalmultidimensional experiments (Cavanagh et al., Protein NMR SpectroscopyAcademic Press: San Diego (1996), which is hereby incorporated byreference in its entirety). ¹⁵N,¹H^(N)-resolved triple resonanceexperiments sequentially linking ¹³C^(α/β) and/or ¹H^(α) shifts are themost widely used (Cavanagh et al., Protein NMR Spectroscopy AcademicPress: San Diego (1996), which is hereby incorporated by reference inits entirety). For (partly) unfolded or α-helical (membrane) proteins,spectral analysis is, however, impeded by very high shift degeneracy, sothat novel methodology for their efficient assignment is required.¹⁵N,¹H^(N)-degeneracy can be largely removed in¹³C′_(i-1),¹⁵N_(i),¹H^(N) _(i)-resolved experiments (i is a residuenumber) (Szyperski et al., J. Magn. Reson. B 109:229-233 (1995); Konratet al., J. Biomol. NMR 15:309-313 (1999), which are hereby incorporatedby reference in their entirety). When using correlated ¹³C^(αβ) or¹³C^(α)/¹H^(α) shifts to establish connectivities, conventional NMR(Cavanagh et al., Protein NMR Spectroscopy Academic Press: San Diego(1996), which is hereby incorporated by reference in its entirety) wouldrequire recording of 5D spectra. Measurement times for such spectra areprohibitively long or lead to “sampling limited” data collection(Szyperski et al., Proc. Natl. Acad. Sci. USA, 99:8009-8014 (2002),which is hereby incorporated by reference in its entirety). G-matrix FT(GFT) NMR (Kim et al., J. Am. Chem. Soc. 125:1385-1393 (2003); Kim etal., J. Biomol. NMR 28:117-130 (2004); Atreya et al., Proc. Natl. Acad.Sci. USA 101:9642-9647 (2004), which are hereby incorporated byreference in their entirety), rooted in reduced-dimensionality NMR(Szyperski et al., J. Am. Chem. Soc. 115:9307-9308 (1993); Brutscher etal., J. Magn. Reson. B109:238-242 (1995); Szyperski et al., J. Am. Chem.Soc. 118:8147-8148 (1996); Löhr et al., J. Biomol. NMR 6:189-195 (1995);Szyperski et al., J. Biomol. NMR 11:387-405 (1998), which are herebyincorporated by reference in their entirety) and related to accordionspectroscopy (Bodenhausen et al., J. Magn. Reson. 45:367-373 (1981);Atreya et al., Methods Enzymol. 394:78-108 (2005), which are herebyincorporated by reference in their entirety), can (i) rapidly provideprecise high-dimensional spectral information and (ii) serve toreconstruct higher-dimensional spectra (Kupce et al., J. Am. Chem. Soc.125:13958-13959 (2003); Coggins et al., J. Am. Chem. Soc. 126:1000-1001(2004), which are hereby incorporated by reference in their entirety).Previously published (4,3)D GFT experiments (Atreya et al., Proc. Natl.Acad. Sci. USA 101:9642-9647 (2004), which is hereby incorporated byreference in its entirety) have greatly increased the speed of NMRstructure determination, but are not optimally tailored for proteinswith very high shift degeneracy.

This example (as well as Examples 2, 3, and 4) discloses “G²FT NMRexperiments” in which two G-matrix transformations were applied. First,¹³C′_(i-1),¹⁵N_(i),¹H^(N) _(i)-resolved experiments were implemented(FIG. 1). ¹⁵N_(i) and ¹³C′_(i-1) shifts were jointly sampled forbreaking ¹⁵N,¹H^(N)-shift degeneracy (Szyperski et al., J. Magn. Reson.B 109:229-233 (1995); Konrat et al., J. Biomol. NMR 15:309-313 (1999),which are hereby incorporated by reference in their entirety), and¹³C^(α/β) and ¹³C^(α) shifts were jointly sampled for sequentiallylinking spin systems (Atreya et al., Proc. Natl. Acad. Sci. USA101:9642-9647 (2004), which is hereby incorporated by reference in itsentirety). Resulting (5,3)D HN{N,CO}{C ^(αβ) C ^(α)} and HN{NCO}{C ^(αβ)C ^(α)} provided, respectively, intraresidue and sequentialconnectivities via one-bond scalar couplings (FIG. 1) based on2*Ω(¹³C^(α)), Ω(¹³C^(α))+Ω(¹³C^(β)) and Ω(¹³C^(α))−Ω(¹³C^(β)) (Atreya etal., Proc. Natl. Acad. Sci. USA 101:9642-9647 (2004), which is herebyincorporated by reference in its entirety). The curly brackets groupjointly sampled shifts represented by underlined letters (Kim et al., J.Am. Chem. Soc. 125:1385-1393 (2003), which is hereby incorporated byreference in its entirety), and in (5,3)D HN{N,CO}{C ^(αβ) C ^(α)} thecomma indicates a bifurcated ¹³C′_(i-1)←¹⁵N_(i)→¹³C^(α) _(i) transfer(Szyperski et al., J. Magn. Reson. B 109:229-233 (1995); Konrat et al.,J. Biomol. NMR 15:309-313 (1999); Szyperski et al., J. Am. Chem. Soc.118:8147-8148 (1996); Szyperski et al., J. Biomol. NMR 11:387-405(1998), which are hereby incorporated by reference in their entirety).

More specifically, in G²FT (5,3)D HN{N,CO}{C ^(αβ) C ^(α)},magnetization from ¹⁵N nucleus of residue i was simultaneouslytransferred to ¹³C′ (¹³CO) of residue i−1 and the ¹³C^(α) of residues iand i−1 (hereafter referred to as i/i−1). Subsequently, ¹³C′_(i-1) wasfrequency labeled jointly with ¹⁵N_(i) during t₂(ω₂), with the latterbeing detected in quadrature. After independent frequency labeling of¹³C^(α) _(i/i-)1 and ¹³C^(β) _(i/i-1) spins during t₁(ω₁), magnetizationwas transferred to the respective ¹³C^(α) _(i/i-1) spin, which was thenfrequency labeled and detected in quadrature during t₁(ω₁). Sequentialapplication of G-matrix transformations along ω₁ and ω₂ yielded fourbasic spectra which can be grouped into two sets, B1 and B2, comprisingpeaks at Ω₀(¹⁵N_(i))±Ω₁(¹³C′_(i-1)) along ω₂. B1 and B2 each contained 2basic spectra comprising peaks at Ω₀(¹³C^(α) _(i))±Ω₁(¹³C^(α/β) _(i))and Ω₀(¹³C^(α) _(i-1))±Ω₁(¹³C^(α/β) _(i-1)) along ω₁. Such a peakpattern is illustrated in FIG. 2.

In G²FT (5,3)D HN{NCO}{C ^(αβ) C ^(α)}, as well as G²FT (5,3)D {C ^(αβ)C ^(α)}{CON}HN, after independent frequency labeling of ¹³C^(α) _(i-1)and ¹³C^(β) _(i-1) spins during t₁(ω₁), magnetization was transferred tothe respective ¹³C^(α) _(i-1) spin, which was then frequency labeled anddetected in quadrature during t₁(ω₁). Subsequently, ¹³C′_(i-1) wasfrequency labeled in conjunction with ¹⁵N_(i) during t₂(ω₂). Sequentialapplication of G-matrix transformations along ω₁ and ω₂ yielded fourbasic spectra as in G²FT (5,3)D HN{N,CO}{C ^(αβ) C ^(α)} above, whichcan be grouped into two sets, B1 and B2 comprising peaks atΩ₀(¹⁵N_(i))±Ω₁(¹³C′_(i-1)) along ω₂. B1 and B2 each contained 2 basicspectra comprising peaks at Ω₀(¹³C^(α) _(i-1))±Ω₁(¹³C^(α/β) _(i-1))along ω₁. Such a peak pattern is illustrated in FIGS. 3 and 4. (5,3)DHN{NCO}{C ^(αβ) C ^(α)} is an “out-and-back” type of experiment, while(5,3)D {C ^(αβ) C ^(α)}{CON}HN is of “out-and-stay” type.

The r.f. pulse schemes of G²FT (5,3)D HN{N,CO}{C ^(αβ) C ^(α))} (FIG. 5)and G²FT (5,3)D HN{NCO}{C ^(αβ) C ^(α)} (FIG. 6) yielded “out-and-back”transfers. This allowed employment of GFT (Kim et al., J. Am. Chem. Soc.125:1385-1393 (2003), which is hereby incorporated by reference in itsentirety)-TROSY (Pervushin et al., Proc. Natl. Acad. Sci. 94:12366-12371(1997), which is hereby incorporated by reference in its entirety) for(large) deuterated (Gardner et al., Annu. Rev. Biophys. Biomol. Struct.27:307-318 (1998), which is hereby incorporated by reference in itsentirety) proteins (embedded in membrane mimics), and enabledlongitudinal ¹H relaxation (L-) optimization (Pervushin et al., J. Am.Chem. Soc. 124:12898-12902 (2002), which is hereby incorporated byreference in its entirety). (5,3)D HN{N,CO}{C ^(αβ) C ^(α)} andHN{NCO}{C ^(αβ) C ^(α)} L-G²FT NMR experiments were performed (Table 1),respectively, in 24 and 20 hours for a ˜0.8 mM solution of ¹⁵N,¹³Cdoubly labeled 17 kDa protein yqbG, target of the Northeast StructuralGenomics consortium, at 25° C. on a Varian INOVA 600 spectrometer (PaloAlto, Calif.) equipped with a cryogenic probe. Processing yielded foursubspectra. Each contained one peak of a quartet atω₁:Ω(¹³C^(α))±Ω(¹³C^(αβ))/ω₂:Ω(¹⁵N)±κΩ(¹³C′). Assignments wereaccomplished in three steps. First, peak pairs at ω₁:Ω(¹⁵N)±κΩ(¹³C′) in(3,2)D HNNCO (FIG. 7; Table 1) were centered about peaks in 2D[¹⁵N,¹H]-HSQC and provided spin system identification. Next, peak pairpositions were transferred to (5,3)D G²FT subspectra, where the same ω₁pattern was observed at ω₂:Ω(¹⁵N)±κΩ(¹³C′). Signals at ω₁:2*Ω(¹³C^(α))were “central peaks” for pair identification at ω₁:Ω(¹³C)±Ω(¹³C^(β))(Atreya et al., Proc. Natl. Acad. Sci. USA 101:9642-9647 (2004), whichis hereby incorporated by reference in its entirety), which profitedfrom increased dispersion along ω₁ due to C^(αβ)C^(α) frequency labeling(Atreya et al., Proc. Natl. Acad. Sci. USA 101:9642-9647 (2004), whichis hereby incorporated by reference in its entirety). Lastly,“sequential walks” at ω₂:Ω(¹⁵N)±κΩ(¹³C′) in two sets of subspectrayielded three connectivities each, i.e., a total of six. TABLE 1Acquisition Parameters for the G²FT NMR Experiments Indirect Figuredimension: number t_(max)(ms); Peak for r.f. Complex points; MeasurementDetection pulse G²FT NMR Experiments Digital Resolution Time Yieldscheme Magnetization transfer pathway Protein (Hz/Pt)^(a) (hrs) (%)  5

yqbG ω₁(¹³C^(α); ¹³C^(αβ)): 6.5; 72; 22 ω₂(¹⁵N; ¹³C′): 24.0; 36; 24 2493 rps24e ω₁(¹³C^(α); ¹³C^(αβ)): 6.5; 90; 27 ω₂(¹⁵N; ¹³C′): 24.0; 40; 277 95  6

yqbG ω₁(¹³C^(α); ¹³C^(αβ)): 6.5; 72; 22 ω₂(¹⁵N; ¹³C′): 24.0; 36; 24 2097 rps24e ω₁(¹³C^(α); ¹³C^(αβ)): 6.5; 90; 27 ω₂(¹⁵N; ¹³C′): 24.0; 40; 277 100 11

yqbG ω₁(¹³C^(α); ¹³C^(αβ)): 6.5; 72; 22 ω₂(¹⁵N; ¹³C′): 24.0; 36; 24 13.5110 18

Z-domain ω₁(¹³C^(α); ¹H^(α)): 6.5; 78; 23 ω₂(¹⁵N; ¹³C′): 16.0; 46; 44 16100 19

Z-domain ω₁(¹³C^(α); ¹³C^(αβ)): 6.5; 28; 23 ω₂(¹⁵N; ¹³C′): 16.0; 46; 4413 100 24

Ubiquitin ω₁(¹³C^(α); ¹³C^(αβ), H^(αβ)): 6.5; 98; 34 ω₂(¹⁵N; ¹³C′):10.0; 30; 47 24 100 13

rps24e ω₁(¹³C^(α); ¹³C^(αβ)): 6.5; 90; 23 ω₂(¹⁵N; ¹³C^(α)): 13.0; 40; 4713 14

rps24e ω₁(¹³C^(α); ¹³C^(αβ)): 6.5; 90; 23 ω₂(¹⁵N; ¹³Cα): 13.0; 40; 47 13^(a)Direct dimension: ω₃(¹H^(N)): 64; 512; 20^(b)Includes a 2D [¹⁵ N-¹H^(N)]HSQC (ω₁(¹⁵N): 80; 128; 15 min) and(3,2)D HNNCO[ω₁(¹⁵N; ¹³C′): 40; 64; 1.5 hrs]

α-Helical protein yqbG exhibited ¹⁵N,¹H^(N)-shift degeneracy in 2D[¹⁵N,¹H]-HSQC (FIGS. 8(a) and 9(a)). This was aggravated at the lowerresolution of 3D spectra (FIGS. 8(b) and 9(b)) where complete degeneracywas observed for eight residues. In contrast, at least one of the twopeaks at ω₂:Ω(¹⁵N)±κΩ(¹³C′) (FIGS. 8(c)-(d) and 9(c)-(d)) were resolvedfor all residues. This allowed efficient sequential assignment using the(5,3)D HN{N,CO}{C ^(αβ) C ^(α)} (peak detection yield: 93%)/HN{NCO}{C^(αβ) C ^(α)} (yield: 95%) experiments (FIG. 10). (For nondeuteratedproteins, (5,3)D {C ^(αβ) C ^(α)}{CON}HN (FIGS. 11 and 12) is often moresensitive then the out-and-back implementation.)

L-optimization (FIG. 5; Pervushin et al., J. Am. Chem. Soc.124:12898-12902 (2002), which is hereby incorporated by reference in itsentirety) can increase sampling speed of out-and-back experimentswithout loss of intrinsic sensitivity (Atreya et al., Proc. Natl. Acad.Sci. USA 101:9642-9647 (2004), which is hereby incorporated by referencein its entirety), yielding minimal measurement times of ˜7 h for (5,3)DHN{N,CO}{C ^(αβ) C ^(α)}/HN{NCO}{C ^(αβ) C ^(α)} (Table 1). A furtherreduction of measurement time can be achieved by maximum entropyreconstruction of nonlinearly sampled data (Atreya et al., MethodsEnzymol. 394:78-108 (2005); Hoch et al., NMR Data Processing Wiley-Liss:New York (1996); Rovnyak et al., J. Magn. Reson. 170:15-21 (2004), whichare hereby incorporated by reference in their entirety), as isdemonstrated herein for 13.5 kDa protein rps24e, target of the NortheastStructural Genomics consortium. L-(5,3)D G²FT HN{NCO}{C ^(αβ) C ^(α)}data were recorded in 3.5 hours, making L-(5,3)D G²FT NMR a viableoption for high-throughput data collection in structural genomics(Montelione et al., Nature Struct. Biol. 7:982-984 (2002), which ishereby incorporated by reference in its entirety).

To enable assignment of systems with very high shift degeneracy,additional G²FT NMR experiments were implemented (see Table 1 andExamples 2, 3, and 4). The (5,3)D G²FT NMR experiments can be combinedwith ¹⁵N-resolved (4,3)D counterparts (Atreya et al., Proc. Natl. Acad.Sci. USA 101:9642-9647 (2004), which is hereby incorporated by referencein its entirety). (¹⁵N-resolved (4,3)D GFT subspectra can be created bysymmetrizing (Szyperski et al., J. Magn. Reson. B 109:229-233 (1995),which is hereby incorporated by reference in its entirety) pairs ofcorresponding (5,3)D G²FT subspectra along ω₁(¹⁵N;¹³C′) about theposition of Ω(¹⁵N), accurately defined in (3,2)D HNNCO). This enablesone to establish sequential walks at ω₂:Ω(¹⁵N)±κΩ(¹³C′) orω₂:Ω(¹⁵N)±κΩ(¹³C^(α)) as well as ω₂:Ω(¹⁵N). (In the three sets ofsubspectra constituting (5,3)D HN{N,CO}{C ^(αβ) C ^(α)}, (5,3)DHN{NCO}{C ^(αβ) C ^(α)}, and (4,3)D HNNC ^(αβ) C ^(α), nine sequentialwalks were established (FIG. 9). Hence, combination of all three pairsof (5,3)D G²FT experiments described in the present application canprovide a total of 24 independent sequential walks.) Taken together, thenovel (5,3)D G²FT NMR experiments are powerful for efficiently assigningproteins with high shift degeneracy and promise to pave the way forNMR-based structural genomics of membrane proteins (Sorgen et al., Proc.Natl. Acad. Sci. USA 99:14037-14040 (2002), which is hereby incorporatedby reference in its entirety).

Example 2 G²FT (5,3)D HN{NC ^(α)}{C ^(αβ) C ^(α)} and G²Fr (5,3)DHN{N(CO)C ^(α)}{C ^(αβ) C ^(α)} NMR Experiments

Experiments profiting from large ¹³C^(α) shift dispersion (Cavanagh etal., Protein NMR Spectroscopy Academic Press: San Diego (1996), which ishereby incorporated by reference in its entirety) were recorded for 13.5kDa protein rps24e. G²FT (5,3)D HN{NC ^(α)}{C ^(αβ) C ^(α)} NMRexperiment (FIG. 13; 13 hrs.; 100%) and G²FT (5,3)D HN{N(CO)C ^(α)}{C^(αβ) C ^(α)} NMR experiment (FIG. 14; 13 hrs.; 100%) enabled¹³C^(α),¹⁵N,¹H^(N)-resolved sequential assignment of backbone ¹³C^(α)and sidechain ¹³C^(β) resonances in proteins (FIG. 15).

In G²FT (5,3)D HN{NC ^(α)}{C ^(αβ) C ^(α)}, magnetization from ¹⁵N_(i)nucleus was transferred to ¹³C^(α) _(i) which was frequency labeledjointly with ¹⁵N_(i) during t₂ (ω₂), the latter being detected inquadrature. Subsequently, after independent frequency labeling of¹³C^(α) _(i/i-1) and ¹³C^(β) _(i/i-1) spins during t₁(ω₁), magnetizationwas transferred to the respective ¹³C^(α) _(i/i-1) spin, which was thenfrequency labeled and detected in quadrature during t₁(ω₁). Sequentialapplication of G-matrix transformations along ω₁ and ω₂ yielded fourbasic spectra which can be grouped into two sets, B1 and B2, comprisingpeaks at Ω₀(¹⁵N_(i))±Ω₁(¹³C^(α) _(i)) along ω₂. B1 and B2 each contained2 basic spectra comprising peaks at ω₀(¹³C^(α) _(i))±Ω₁(¹³C^(α/β) _(i))and Ω₀(¹³C^(α) _(i-1))±Ω₁(¹³C^(α/β) _(i-1)) along ω₁. Such a peakpattern is illustrated in FIG. 16.

In G²FT (5,3)D HN{N(CO)C ^(α)}{C ^(αβ) C ^(α)}, after independentfrequency labeling of ¹³C^(α) _(i-1) and ¹³C^(β) _(i-1) spins duringt₁(ω₁), magnetization was transferred to the respective ¹³C^(α) _(i-1)spin, which was then frequency labeled and detected in quadrature duringt₁(ω₁). Subsequently, ¹³C^(α) _(i-1) was frequency labeled inconjunction with ¹⁵N_(i) during t₂(ω₂). Sequential application ofG-matrix transformations along ω₁ and ω₂ yielded four basic spectrawhich can be grouped into two sets, B1 and B2, comprising peaks atΩ₀(¹⁵N_(i))±Ω₁(¹³C^(α) _(i-1)) along ω₂. B1 and B2 each contained 2basic spectra comprising peaks at Ω₀(¹³C^(α) _(i-1))±Ω₁(¹³C^(α/β)_(i-1)) along ω₁. Such a peak pattern is illustrated in FIG. 17.

Example 3 G²FT (5,3)D HN{N,CO}{C ^(α) H ^(α)} and G²FT (5,3)D {H ^(α) C^(α)}{CON}HN NMR Experiments

G²FT (5,3)D HN{N,CO}{C ^(α) Hα} (FIG. 18; measurement time 16 hrs.; peakdetection yield: 100%) and G²FT (5,3)D {H^(α)C^(α)}{CON}HN (FIG. 19; 13hrs.; 100%) were recorded for 8 kDa protein Z-domain (Tashiro et al., J.Mol. Biol. 272:573-590 (1997), which is hereby incorporated by referencein its entirety), which allowed ¹³C′_(i-1),¹⁵N_(i),¹H^(N) _(i)-resolvedsequential assignment based on Ω(¹³C^(α)) and Ω(¹H^(α)) (FIG. 20).

In G²FT (5,3)D HN{N,CO}{C ^(α) H ^(α)}, magnetization from ¹⁵N nucleusof residue i was simultaneously transferred to ¹³C′ of residue i−1 andthe ¹³C^(α) of residues i/i−1. Subsequently, ¹³C′_(i-1) was frequencylabeled jointly with ¹⁵N_(i) during t₂(ω₂) with the latter detected inquadrature. ¹³C^(α) _(i/i-1) and ¹H^(α) _(i/i-1) spins were jointlysampled during t₁(ω₁) with ¹³C^(α) being detected in quadrature.Sequential application of G-matrix transformations along ω₁ and ω₂yielded four basic spectra which can be grouped into two sets, B1 andB2, comprising peaks at Ω₀(¹⁵N_(i))±Ω₁(¹³C′_(i-1)) along ω₂. B1 and B2each contained 2 basic spectra comprising peaks at Ω₀(¹³C^(α)_(i))±Ω₁(¹H^(α) _(i)) and Ω₀(¹³C^(α) _(i-1))±Ω₁(¹H^(α) _(i-1)) along ω¹.Such a peak pattern is illustrated in FIG. 21. Using the principlediscussed above, the first order central peak spectra comprising peaksat Ω₀(¹³C^(α) _(i)) along ω₁ was obtained using (4,3)D HN{N,CO}{C^(α)}.In this experiment, the transfer of magnetization from ¹³C^(α) _(i/i-1)to ¹H^(α) _(i/i-1) and back was omitted. The r.f. pulse scheme for(4,3)D HN{N,CO}{C^(α)} is shown in FIG. 22.

In G²FT (5,3)D {H ^(α) C ^(α)}{CON}HN, ¹H^(α) _(i-1) and ¹³C^(α) _(i-1)spins were jointly sampled during t₁(ω₁), with the latter being detectedin quadrature. Subsequently, magnetization was transferred to ¹³C′_(i-1)which was frequency labeled jointly with ¹⁵N_(i) during t₂(ω₂).Sequential application of G-matrix transformations along ω₁ and ω₂yielded four basic spectra which can be grouped into two sets, B1 andB2, comprising peaks at Ω₀(¹⁵N_(i))±Ω₁(¹³C′_(i-1)) along ω₂. B1 and B2each contained 2 basic spectra comprising peaks at Ω₀(¹³C^(α)_(i-1))±Ω₁(¹H^(α) _(i-1)) along ω₁. Such a peak pattern is illustratedin FIG. 23. The two first order central peak spectra can be obtainedeither by omission of ¹H^(α) _(i-1) frequency labeling along ω₁ or byusing ¹³C steady-state magnetization.

Example 4 G²FT (6,3)D {H ^(αβ) C ^(αβ) C ^(α)}{CON}HN NMR Experiment

Having obtained the chemical shifts of ¹³C^(α/β) spins for a given aminoacid residue using the G²FT (5,3)D HN{N,CO}{C ^(αβ) C ^(α)}, G²FT (5,3)DHN{NCO}{C ^(αβ) C ^(α)}, G²FT (5,3)D HN{NC ^(α)}{C ^(αβ) C ^(α)}, andG²FT (5,3)D HN{N(CO)C ^(α)}{C ^(αβ) C ^(α)} NMR experiments, G²FT (6,3)D{H ^(αβ) C ^(αβ) C ^(α)}{CON}HN (FIGS. 24 and 25; 24 hrs.; 100%) wasrecorded for 9 kDa protein ubiquitin, which allowed the assignment of¹H^(αβ).

In G²FT (6,3)D {H ^(αβ) C ^(αβ) C ^(α)}{CON}HN, frequency labeling ofthe ¹H^(α/β) _(i-1) spin was carried out simultaneously with that of¹³C^(α/β) _(i-1) and ¹³C^(α) _(i-1) spins. Subsequently, ¹³C′_(i-1) wasfrequency labeled in conjunction with ¹⁵N_(i) during t₂(ω₂). Sequentialapplication of G-matrix transformations along ω₁ and ω₂ yielded eightbasic spectra which can be grouped into two sets, B1 and B2, comprisingpeaks at Ω₀(¹⁵N_(i))±Ω₁(¹³C′_(i-1)) along ω₂. B1 and B2 each contained 4basic spectra comprising peaks at Ω₀(¹³C^(α) _(i-1))±Ω₁(¹³C^(α/β)_(i-1))±Ω₂(¹H^(α/β) _(i-1)) along ω₁. The four first order central peakspectra were identical to the spectra from the above-described G²FT(5,3)D HN{NCO}{C ^(αβ) C ^(α)} and were obtained either by omission of¹H^(α/β) _(i-1) frequency labeling along a), or by using ¹³Csteady-state magnetization.

Example 5 GFT (5,3)D HC(C)C—CH NMR Experiment

As was shown for (4,3)D GFT congeners (Atreya et al., Proc. Natl. Acad.Sci. USA 101:9642-9647 (2004), which is hereby incorporated by referencein its entirety), C^(αβ)C^(α)-type G²FT experiments can be combined witha GFT (5,3)D HC(C)C—CH NMR experiment for aliphatic side chainassignment. The peak patterns observed in a GFT (5,3)D HC(C)C—CH NMRexperiment are illustrated in FIG. 26 and the r.f. pulse scheme for thatexperiment is shown in FIG. 27. Acquisition parameters for the GFT(5,3)D HC(C)C—CH NM experiment are shown in Table 2. ¹³C steady-statemagnetization was used to obtain the two first order central peakspectra. The GFT (5,3)D HC(C)C—CH NMR experiment can also be used forassigning backbone sugar resonances in ¹³C-labeled oligonucleotides bytuning the constant time delay to a value suited for transferringmagnetization between ¹³C-spins in nucleic acids. TABLE 2 AcquisitionParameters for the GFT (5,3)D HC(C)C—CH NMR Experiment Recorded for 14kDa Protein PfR13 GFT (5,3)D HC(C)C—CH ¹H resonance frequency 750 MHzNo. of Points (t₁, t₂, t₃) Collected: 140, 24, 512 After LP: 140, 24,512 After zero filling: 512, 64, 1024 Window functions: sine 70/70/70No. of transients: 2  Spectral width (ω₁, ω₂, ω₃; Hz) 26000, 5600, 8000t_(max) (ms) 5.5, 4.2, 64.0 Carrier Position (ω₁, ω₂, ω₃; ppm) 43/0.0,43.0, 4.78 Recycle delay(s)  0.4 Collection time (hrs) 28.0

Example 6 Longitudinal Proton Relaxation (L-) Optimization for¹H^(aromatic)—¹³C^(aromatic) Correlation Spectroscopy Explored by Use of2D [¹³C,¹H]-HSQC/TROSY

¹H^(aromatic) L-optimization was explored for a sample of a NortheastStructural Genomics Consortium (NESG) target protein PfR13 (14 kDa) at¹H resonance frequency of 750 MHz. Two series of experiments (with andwithout) L-optimization, L- and non-L-ct 2D [¹³C,¹H]-HSQC/TROSY, wereperformed at 20° C. and 4° C., using pulsed field gradient(PFG)-preservation of equivalent pathways (PEP) sensitivity-enhanced(Cavanagh et al., Protein NMR Spectroscopy: Principles and PracticeAcademic Press: San Diego (1996), which is hereby incorporated byreference in its entirety) 2D [¹³C,¹H]-HSQC and 2D [¹³C,¹H]-TROSY r.f.pulse schemes (FIG. 28). (PFG-PEP is recommended for all but very largeproteins; sensitivity is enhanced up to τ_(iso)˜35 ns (FIG. 29) withexcellent water suppression. TROSY is generally preferred in 2D ct[¹³C,¹H]-spectroscopy since sensitivity can be enhanced by using¹³C^(aromatic) polarization (Pervushin et al., J. Am. Chem. Soc.120:6394-6400 (1998), which is hereby incorporated by reference in itsentirety). See Example 7.) The following t_(rel) values were used at 4°C.: 0.1, 0.2, 0.3, 0.4, 0.6, 0.8, 1.0, 1.2, 1.4, 1.6, 2.0, and 3.0 s,and at 20° C.: 0.25, 0.32, 0.4, 0.6, 0.8, 1.0, 1.2, 1.4, 1.6, 2.0, and3.0 s. HSQC spectra were recorded at 20° C. with varying relaxationdelay between scans, where the approximate isotropic correlation timefor overall tumbling of PfR13, τ_(iso), is 8.5 ns. TROSY spectra withsuppression of signal contributions from ¹³C^(aromatic) polarizationwere acquired at 4° C., where τ_(iso)=12.5 ns. Signal-to-noise (S/N)ratios were measured as a function of the relaxation delay betweenscans, t_(rel), and divided by the square-root of the measurement time,t_(tot), thus yielding SN_(t), a measure for intrinsic sensitivity. Aleast-squares fit of $\begin{matrix}{{SN}_{t} = {A\frac{1 - {\exp\left( {- {R_{1}\left( {t_{rel} + t_{acq}} \right)}} \right)}}{\sqrt{t_{rel} + t_{acq} + t_{seq}}}}} & (1)\end{matrix}$

to the experimental SN_(t) values yielded t_(rel) ^(opt) at which, for agiven proton, intrinsic sensitivity was maximal (Tables 3, 4, and 5).t_(acq) and t_(seq) represent the acquisition time and length of thepulsing period, respectively, while scaling factor A and effectivelongitudinal relaxation rate R₁ are fitted. Twenty two and twentywell-resolved cross-peaks were considered from the 20° C. and 4° C.spectra, respectively. Representative experimental data and fittedcurves are shown in FIG. 30, and Tables 3 and 4 afford a listing ofparameters for each of the analyzed ¹H^(aromatic) spins. Moreover, Table5 provides a survey of parameters averaged according to residue type.Analysis of resolved peaks (Tables 3 and 4) revealed that at 20° C. (4°C.) (i) the average t_(rel) ^(opt)=1.9 s (1.8 s) without is longer thanthe average t_(rel) ^(opt)=1.1 s (1.0 s) with L-optimization, and (ii)the average gain in intrinsic sensitivity arising at t_(rel) ^(opt) dueto L-optimization (FIG. 30) is ˜20% (˜15%). For the L-optimizedexperiment acquired at t_(rel) ^(match)˜0.4-0.6 s, intrinsic sensitivitymatches the one of the non-L congener at its t_(rel) ^(opt), that is,L-optimization allows one to reach the maximum sensitivity achievedwithout L-optimization at about 4-fold increased sampling speed. TABLE 3Comparison of 2D [¹³C, ¹H]-HSQC Acquired for PfR13 at 20° C. with andwithout L-optimization Without L-optimization With L-optimizationResidue Res. Atom SN_(t) ^(a) SN_(t) ^(a) Ratio^(c) of No. Type Type AR₁ [s⁻¹] t_(rel) ^(opt) [s] at t_(rel) ^(opt) A R₁ [s⁻¹] t_(rel) ^(opt)[s] at t_(rel) ^(opt) t_(rel) ^(match) [s]^(b) SN_(t) at t_(rel) ^(opt)3 Trp H^(δ1) 334 ± 28 0.5 ± 0.06 2.6 146 259 ± 8 1.0 ± 0.06 1.3 162 0.51.10 3 Trp H^(ε3) 223 ± 11 0.6 ± 0.04 2.2 107 197 ± 6 0.9 ± 0.05 1.3 1200.5 1.10 3 Trp H^(η2) 272 ± 11 0.6 ± 0.04 2.1 133 240 ± 7 0.9 ± 0.05 1.4145 0.6 1.10 3 Trp H^(ζ2) 303 ± 23 0.5 ± 0.06 2.4 139 251 ± 6 1.0 ± 0.041.2 160 0.5 1.15 3 Trp H^(ζ3) 393 ± 21 0.5 ± 0.04 2.4 181  344 ± 16 0.8± 0.06 1.5 193 0.8 1.05 11 Phe H^(δ) 857 ± 6  0.9 ± 0.01 1.4 505  839 ±10 1.3 ± 0.03 1.0 590 0.3 1.15 11 Phe H^(ε) 1014 ± 6  0.9 ± 0.01 1.4 602 942 ± 13 1.2 ± 0.03 1.0 655 0.5 1.10 11 Phe H^(ζ) 249 ± 8  0.8 ± 0.051.5 144 244 ± 6 1.2 ± 0.05 1.1 164 0.4 1.15 21 Tyr H^(δ) 110 ± 7  0.7 ±0.06 1.8 58 104 ± 3 1.3 ± 0.08 1.0 73 0.3 1.25 21 Tyr H^(ε) 477 ± 4  0.8± 0.01 1.6 264 472 ± 3 1.5 ± 0.02 0.9 355 0.2 1.35 42 Phe H^(δ) 317 ± 130.7 ± 0.04 1.9 161 273 ± 5 1.2 ± 0.04 1.0 187 0.4 1.15 42 Phe H^(ε) 232± 3  0.9 ± 0.02 1.4 138 220 ± 3 1.1 ± 0.03 1.1 147 0.6 1.05 60 Phe H^(ε)82 ± 6 0.6 ± 0.06 2.3 38  84 ± 6 0.8 ± 0.08 1.6 47 0.5 1.20 86 Tyr H^(ε)467 ± 4  0.7 ± 0.01 1.7 254 466 ± 3 1.4 ± 0.02 0.9 346 0.2 1.35 89 PheH^(δ) 186 ± 10 0.7 ± 0.05 1.9 95 173 ± 3 1.4 ± 0.06 0.9 128 0.2 1.35 89Phe H^(ζ) 79 ± 4 0.9 ± 0.07 1.4 47  84 ± 3 1.1 ± 0.06 1.2 54 0.4 1.15 90Tyr H^(δ) 442 ± 17 0.5 ± 0.03 2.4 203  397 ± 10 0.9 ± 0.04 1.3 240 0.51.20 90 Tyr H^(ε) 415 ± 20 0.5 ± 0.03 2.6 183 370 ± 5 1.1 ± 0.03 1.1 2470.2 1.35 98 Tyr H^(δ) 924 ± 32 0.7 ± 0.04 1.9 474  874 ± 14 1.1 ± 0.041.1 580 0.3 1.20 98 Tyr H^(ε) 1630 ± 41  0.7 ± 0.03 1.8 867 1667 ± 231.3 ± 0.03 1.00 1164 0.2 1.35 110 Tyr H^(δ) 3371 ± 12  1.1 ± 0.01 1.12256 3316 ± 31 1.4 ± 0.03 0.9 2455 0.4 1.10 110 Tyr H^(ε) 3746 ± 11  1.2± 0.01 1.1 2524 4009 ± 48 1.3 ± 0.03 0.9 2882 0.4 1.15^(a)The standard deviation of the noise of the spectra (assumed to be“white”) was scaled to (an arbitrarily chosen) level of 100. Then, thepeak height was taken and divided by the square-root of the measurementtime (in seconds).^(b)t_(rel) at which SN_(t) in spectra acquired with L-optimizationmatches the maximum SN_(t) at t_(rel) ^(opt) in spectra acquired withoutL-optimization.^(c)Ratio of SN_(t) in L-optimized HSQC over that in HSQC withoutL-optimization at respective t_(rel) ^(opt).

TABLE 4 Comparison of 2D [¹³C, ¹H]-TROSY Acquired for PfR13 at 4° C.with and without L-optimization Without L-optimization WithL-optimization Residue Atom SN_(t) ^(a) SN_(t) ^(a) Ratio^(c) of No.Res. Type A R₁ [s⁻¹] t_(rel) ^(opt) [s] at t_(rel) ^(opt) A R₁ [s⁻¹]t_(rel) ^(opt) [s] at t_(rel) ^(opt) t_(rel) ^(match) [s]^(b) SN_(t) att_(rel) ^(opt) 3 Trp H^(δ1) 36 ± 3 0.7 ± 0.09 1.8 19 27 ± 3 1.4 ± 0.220.9 20 0.5 1.05 3 Trp H^(ε3) 47 ± 4 0.7 ± 0.09 1.9 24 43 ± 3 1.2 ± 0.141.1 29 0.4 1.20 3 Trp H^(η2) 59 ± 9 0.6 ± 0.14 2.1 29 52 ± 3 0.9 ± 0.091.4 31 0.7 1.05 3 Trp H^(ζ2) 48 ± 3 0.7 ± 0.07 1.8 26 51 ± 4 0.9 ± 0.111.4 31 0.5 1.20 3 Trp H^(ζ3) 80 ± 9 0.6 ± 0.10 2.0 40 70 ± 3 0.9 ± 0.071.3 43 0.7 1.10 11 Phe H^(ε) 239 ± 9  0.8 ± 0.05 1.5 138 229 ± 5  1.3 ±0.05 1.0 162 0.3 1.20 27 Tyr H^(ε) 100 ± 4  0.9 ± 0.06 1.4 60 81 ± 1 1.6± 0.04 0.8 64 0.4 1.05 42 Phe H^(δ) 76 ± 8 0.7 ± 0.11 1.8 40 60 ± 1 1.4± 0.04 0.9 44 0.4 1.10 42 Phe H^(ε) 96 ± 6 0.7 ± 0.07 1.7 52 82 ± 5 1.1± 0.13 1.2 54 0.8 1.05 57 Tyr H^(ε) 61 ± 4 0.9 ± 0.09 1.5 36 50 ± 1 1.6± 0.08 0.8 39 0.3 1.10 86 Tyr H^(ε) 53 ± 2 0.8 ± 0.06 1.6 30 37 ± 2 1.9± 0.18 0.7 31 0.4 1.05 89 Phe H^(δ) 29 ± 3 0.8 ± 0.15 1.5 17 25 ± 1 1.8± 0.17 0.7 21 0.2 1.25 89 Phe H^(ε)  82 ± 10 0.7 ± 0.12 1.8 42 81 ± 41.1 ± 0.09 1.1 53 0.3 1.25 89 Phe H^(ζ) 45 ± 3 0.8 ± 0.08 1.7 25 44 ± 30.9 ± 0.10 1.4 27 0.7 1.05 90 Tyr H^(δ)  57 ± 10 0.5 ± 0.11 2.6 25 45 ±2 1.1 ± 0.07 1.2 29 0.4 1.15 90 Tyr H^(ε) 57 ± 6 0.7 ± 0.11 1.9 29 50 ±3 1.2 ± 0.13 1.1 34 0.4 1.15 98 Tyr H^(δ) 197 ± 14 0.7 ± 0.08 1.8 103192 ± 5  1.1 ± 0.05 1.1 127 0.3 1.25 98 Tyr H^(ε) 325 ± 16 0.7 ± 0.061.7 176 289 ± 6  1.3 ± 0.05 0.9 207 0.3 1.15 110 Tyr H^(δ) 838 ± 47 0.9± 0.08 1.5 486 784 ± 30 1.2 ± 0.09 1.0 543 0.4 1.10 110 Tyr H^(ε) 767 ±25 0.9 ± 0.05 1.3 471 718 ± 17 1.4 ± 0.06 0.9 526 0.4 1.10^(a)The standard deviation of the noise of the spectra (assumed to be“white”) was scaled to (an arbitrarily chosen) level of 100. Then, thepeak height was taken and divided by the square-root of the measurementtime (in seconds).^(b)t_(rel) at which SN_(t) in spectra acquired with L-optimizationmatches the maximum SN_(t) at t_(rel) ^(opt) in spectra acquired withoutL-optimization.^(c)Ratio of SN_(t) in L-optimized HSQC over that in HSQC withoutL-optimization at respective t_(rel) ^(opt).

TABLE 5 Parameters Averaged According to Residue Type Without WithL-opti- L-opti- Ratio of Temp Residue mization mization t_(rel) ^(match)SN_(t) [° C.] Type t_(rel) ^(opt) [s] t_(rel) ^(opt) [s] [s]^(a) att_(rel) ^(opt) 20 All^(b) 1.9 ± 0.4 1.2 ± 0.2 0.4 ± 0.2 1.20 ± 0.10 Phe1.7 ± 0.3 1.1 ± 0.2 0.4 ± 0.1 1.15 ± 0.09 Trp 2.3 ± 0.2 1.4 ± 0.1 0.6 ±0.1 1.10 ± 0.03 Tyr^(b) 2.0 ± 0.4 1.0 ± 0.2 0.3 ± 0.1 1.30 ± 0.07 4All^(b) 1.8 ± 0.3 1.1 ± 0.2 0.4 ± 0.2 1.15 ± 0.07 Phe 1.7 ± 0.1 1.0 ±0.2 0.5 ± 0.2 1.15 ± 0.09 Trp 1.9 ± 0.1 1.2 ± 0.2 0.5 ± 0.2 1.10 ± 0.07Tyr^(b) 1.8 ± 0.4 0.9 ± 0.2  0.4 ± 0.04 1.15 ± 0.07^(a)t_(rel) at which SN_(t) in spectra acquired with L-optimizationmatches the maximum SN_(t) at t_(rel) ^(opt) in spectra acquired withoutL-optimization.^(b)The C-terminal residue Tyr 110 was excluded.

Example 7 Analysis of PFG-PEP and TROSY Based Sensitivity Enhancement

To assess the role of PFG-PEP and TROSY for sensitivity enhancement in¹H^(aromatic)—¹³C^(aromatic) correlation spectroscopy, theoreticalcalculations of nuclear spin relaxation rates were performed usingsemi-classical relaxation theory (Abragam, Principles of NuclearMagnetism Oxford University Press: New York (1961), which is herebyincorporated by reference in its entirety).

Rates were estimated for a Phe CH^(ε/ζ) moiety with bond lengthsr_(CH)=1.38 Å and r_(CC)=1.09 Å (Weast, CRC Handbook of Chemistry andPhysics CRC Press: Boca Raton, Fla. (1988), which is hereby incorporatedby reference in its entirety), where ¹H^(aromatic) is dipolar coupled totwo vicinal protons at r_(HH)=2.47 Å. The influence of “remotelylocated” protons was estimated by considering the NMR structure of PfR13(PDB code: 1S04). On average, 15 remote protons were located within asphere of 5 Å radius around ¹H^(aromatic), and “<r⁻⁶>-averaging”revealed <r_(HH)>=3.1 Å. For chemical shift anisotropy (CSA) relaxation,the principal components of the CSA tensor of ¹³C^(aromatic) wereassumed to be (Veeman, Prog. NMR Spectrosc. 16:193-235 (1984), which ishereby incorporated by reference in its entirety): σ₁₁=255 ppm, σ₂₂=149ppm, and σ₃₃=15 ppm.

For the calculations, the rigid-body approximation was used (Cavanagh etal., Protein NMR Spectroscopy: Principles and Practice Academic Press:San Diego (1996), which is hereby incorporated by reference in itsentirety), that is, internal motional modes were neglected, and rateswere obtained using the equations listed in Tables 5.5 and 5.7 ofCavanagh et al., Protein NMR Spectroscopy: Principles and PracticeAcademic Press: San Diego (1996), which is hereby incorporated byreference in its entirety, and equations from Pervushin et al., J. Am.Chem. Soc. 120:6394-6400 (1998), which is hereby incorporated byreference in its entirety: $\begin{matrix}{R_{2}^{C} = {{\frac{1}{18}\left( {\gamma_{C}B_{0}\Delta\quad\sigma_{C}} \right)^{2}\left\{ {{J(0)} + {3{J\left( \omega_{C} \right)}}} \right\}} + {\frac{1}{8}\left( {\frac{\mu_{0}}{4\pi}\frac{{\hslash\gamma}_{H}\gamma_{C}}{r_{CH}^{3}}} \right)^{2}\left\{ {{4{J(0)}} + {J\left( {\omega_{H} - \omega_{C}} \right)} + {3{J\left( \omega_{C} \right)}} + {3{J\left( \omega_{H} \right)}} + {6{J\left( {\omega_{H} + \omega_{C}} \right)}}} \right\}}}} & (12) \\{R_{2}^{C,{TROSY}} = {{\frac{1}{18}\left( {\gamma_{C}B_{0}\Delta\quad\sigma_{C}} \right)^{2}\left\{ {{J\left( \omega_{C} \right)} + {2{J\left( {2\omega_{C}} \right)}}} \right\}} + {\frac{1}{8}\left( {\frac{\mu_{0}}{4\pi}\frac{{\hslash\gamma}_{H}\gamma_{C}}{r_{CH}^{3}}} \right)^{2}\left\{ {{4{J(0)}} + {J\left( {\omega_{H} - \omega_{C}} \right)} + {3{J\left( \omega_{C} \right)}} + {3{J\left( \omega_{H} \right)}} + {6{J\left( {\omega_{H} + \omega_{C}} \right)}}} \right\}} - {\frac{1}{12}\left( {\gamma_{C}{B_{0}\left( {\sigma_{33} + \sigma_{22} - {2\sigma_{11}}} \right)}} \right)\left( {\frac{\mu_{0}}{4\pi}\frac{{\hslash\gamma}_{H}\gamma_{C}}{r_{CH}^{3}}} \right)\left\{ {{4{J(0)}} + {3{J\left( \omega_{C} \right)}}} \right\}}}} & (13) \\{R_{2}^{H} = {{\frac{1}{8}\frac{1}{8}\left( {\frac{\mu_{0}}{4\pi}\frac{{\hslash\gamma}_{H}\gamma_{C}}{r_{CH}^{3}}} \right)^{2}\left\{ {{4{J(0)}} + {J\left( {\omega_{H} - \omega_{C}} \right)} + {3{J\left( \omega_{C} \right)}} + {3{J\left( \omega_{H} \right)}} + {6{J\left( {\omega_{H} + \omega_{C}} \right)}}} \right\}} + {\left( {{2\frac{1}{8}\left( {\frac{\mu_{0}}{4\pi}\frac{{\hslash\gamma}_{H}^{2}}{r_{HH}^{3}}} \right)^{2}} + {15\frac{1}{8}\left( {\frac{\mu_{0}}{4\pi}\frac{{\hslash\gamma}_{H}^{2}}{< r_{HH} >^{3}}} \right)^{2}}} \right)\left\{ {{5{J(0)}} + {6{J\left( \omega_{H} \right)}} + {6{J\left( \omega_{H} \right)}} + {6{J\left( {2\omega_{H}} \right)}}} \right\}}}} & (14) \\{{R_{2}^{MQ} = {{\frac{1}{18}\left( {\gamma_{C}B_{0}\Delta\quad\sigma_{C}} \right)^{2}\left\{ {{J\left( \omega_{C} \right)} + {2{J\left( {2\omega_{C}} \right)}}} \right\}} + {\left( {{2\frac{1}{8}\left( {\frac{\mu_{0}}{4\pi}\frac{{\hslash\gamma}_{H}^{2}}{r_{HH}^{3}}} \right)^{2}} + {15\frac{1}{8}\left( {\frac{\mu_{0}}{4\pi}\frac{{\hslash\gamma}_{H}^{2}}{< r_{HH} >^{3}}} \right)^{2}}} \right)\left\{ {{5{J(0)}} + {6{J\left( \omega_{H} \right)}} + {6{J\left( {2\omega_{H}} \right)}}} \right\}}}},{with}} & (15) \\{{\Delta\quad\sigma_{C}} = {\sqrt{\left( {\sigma_{33} - \sigma_{11}} \right)^{2} + \left( {\sigma_{22} - \sigma_{11}} \right)^{2} - {\left( {\sigma_{33} - \sigma_{11}} \right)\left( {\sigma_{22} - \sigma_{11}} \right)}}.}} & (16)\end{matrix}$

As expected, the dominant contributions to the ¹³C^(aromatic)single-quantum relaxation rates (R₂ ^(C), R₂ ^(C,TROSY)) were (i)¹³C^(aromatic) CSA and (ii) dipolar coupling to attached ¹H^(aromatic).The dominant contributions to ¹H^(aromatic) single-quantum relaxation(R₂ ^(H)) were dipolar couplings to the (i) attached ¹³C^(aromatic),(ii) two vicinal ¹H^(aromatic) and (iii) “remote” ¹H spins (see above).The dominant contributions to ¹H^(aromatic)—¹³C^(aromatic)multiple-quantum relaxation rate (R₂ ^(MQ)) were (i) ¹³C CSA and (ii)dipolar couplings between ¹H^(aromatic) and the two vicinal and “remote”¹H. In the following, the impact of isotropic overall tumblingcharacterized by a single correlation time, τ_(iso), on efficiency ofPFG-PEP and TROSY for CH^(aromatic)-moieties was assessed.

PFG-PEP

Neglecting transverse nuclear spin relaxation and signal de-phasing dueto passive scalar couplings, PFG-PEP (Cavanagh et al., Protein NMRSpectroscopy: Principles and Practice Academic Press: San Diego (1996);Kay et al., J. Am. Chem. Soc. 114:10663-10665 (1992), which are herebyincorporated by reference in their entirety) increases sensitivity by √2when compared to conventional data acquisition. When considering (i)de-phasing due to ¹J_(CC) (˜50 Hz) and (ii) transverse relaxation for anisotropically reorienting rigid protein (see equations above), thesensitivity of a PFG-PEP experiment (I_(SE)) relative to theconventional experiment (I₀) is given by: $\begin{matrix}{{{I_{SE}/I_{0}} = {{\sqrt{2} \cdot \left\{ {\frac{1}{2} + {\frac{1}{2}{\exp\left( {{- R_{2}^{MQ}}\tau} \right)}{\cos^{2}\left( {\pi^{1}J_{CC}\tau} \right)}}} \right\}}{\exp\left( {{{- R_{2}^{H}} \cdot 2}ɛ} \right)}}},} & (17)\end{matrix}$where 2ε is the duration of the gradient echo period before the start ofsignal detection and τ is the delay for reverse INEPT (FIG. 28). WithoutPFG-PEP, τ is tuned for maximal polarization transfer according to$\begin{matrix}{{\tau = {\frac{1}{\pi^{1}J_{CH}}{arc}\quad\tan\frac{\pi^{1}J_{CH}}{R_{2}^{C}}}},} & (18)\end{matrix}$where ¹J_(CH)=160 Hz represents the one-bond¹³C^(aromatic)—¹H^(aromatic) scalar coupling.

Then, the sensitivity ratio I_(SE)/I₀ can be calculated as a function ofτ_(iso) (FIG. 29). The calculations suggested that PFG-PEP yields asensitivity gain for τ_(iso) up to ˜35 ns (corresponding to ˜70 kDa atambient temperature in aqueous solution), provided that the gradientecho length 2ε (FIG. 28) is minimized (e.g., set to 200 μs).

TROSY

For assessment of TROSY, a possible contribution to signals arising from¹³C^(aromatic) steady-state polarization was neglected (which can beused in GFT-TROSY (4,3)D HCCH for detecting central peaks but not forenhancing signals arising from ¹H polarization). The sensitivity gainover the non-TROSY experiment for a constant-time chemical shiftevolution period 2T (FIG. 28) is then given by: $\begin{matrix}{{I_{TROSY}/I_{{conv}.}} = {\frac{1}{2}{\frac{\exp\left( {{{- R_{2}^{C,{TROSY}}} \cdot 2}T} \right)}{\exp\left( {{{- R_{2}^{C}} \cdot 2}T} \right)}.}}} & (19)\end{matrix}$The factor ½ reflects the fact that only one of the two doubletcomponents is selected in TROSY. FIG. 31 shows this ratio as a functionof τ_(iso) for the two typically used values for the constant-timeevolution period in HCCH. The calculations predict that TROSY becomesmore sensitive at τ_(iso)>23 ns and τ_(iso)>8 ns when using 4.5 ms(¼J_(CC)) and 13.5 ms (¾J_(CC)) ct evolution periods, respectively (FIG.31). Hence, non-TROSY was more sensitive with medium-sized proteins atthe shorter period (¼J_(CC)) sufficient for GFT (4,3)D HCCH (see Example8).

Example 8 (4,3)D HCCH Experiment: Implementation and Comparison

Exploration of L-optimization with 2D NMR (FIG. 30; Tables 3, 4, and 5)enabled implementation of L-GFT-TROSY (4,3)D HCCH, which is based onhighly efficient ¹H⁽¹⁾(t₁)→¹³C⁽¹⁾(t₁)→¹³C⁽²⁾(t₂)→¹H⁽²⁾(t₃) transfer vialarge ¹J{¹³C^(aromatic)—¹³C^(aromatic)} (˜50 Hz) and¹J{¹H^(aromatic)—¹³C^(aromatic)} (˜160 Hz) couplings. R.f. pulse schemesfor L-GFT and L-GFT-TROSY (4,3)D HCCH are provided in FIG. 32.

An S³-filter (Meissner et al., J. Magn. Reson. 139:447-450 (1999), whichis hereby incorporated by reference in its entirety) was used forsuppressing the faster relaxing (“anti-TROSY”) component in L-GFT-TROSY(4,3)D HCCH. This filter turned out to be superior in terms ofsensitivity when compared with the TROSY implementation of Pervushin etal., J. Am. Chem. Soc. 120:6394-6400 (1998), which is herebyincorporated by reference in its entirety. However, the S³-filter led toa slight reduction in TROSY sensitivity enhancement due to partialexchange of the TROSY/anti-TROSY components in every alternate scan(FIG. 32). It is notable that “active” suppression of the anti-TROSYcomponent can be omitted when employing the longer chemical shiftevolution periods [e.g., t_(1,max)(¹³C/¹H)=13.5 ms] for large proteins.

A technical comment relates to the line-shapes of peaks in the centralpeak subspectrum of L-GFT-TROSY which were derived from polarization ofquaternary carbons (FIG. 33). For CH^(aromatic)-moieties, the two scansallowing cancellation of the anti-TROSY component can be brieflydescribed as:

Quaternary carbon spins, however, do not evolve under ¹J_(CH) couplingand yield C_(y) in every odd-numbered transient prior to t₁(¹³C). Hence,addition of the two scans yields a mixed phase resulting from thesuperposition of an absorptive and a dispersive signal.

The shifts of ¹H⁽¹⁾ and ¹³C⁽¹⁾ were jointly sampled in a GFT dimension.Frequency labeling with the shifts of ¹H⁽¹⁾, ¹³C⁽¹⁾ and ¹³C⁽²⁾ wasaccomplished within only ˜11.6-13.5 ms during polarization transfer.Short maximal evolution times of ˜4.5 ms suffice in the GFT dimensionsince peaks are dispersed over the sum of ¹H^(aromatic) and¹³C^(aromatic) spectral widths (Atreya et al., Proc. Natl. Acad. Sci.USA. 101:9642-9647 (2004), which is hereby incorporated by reference inits entirety). At 4.5 ms ct delay, TROSY yielded higher sensitivity onlyfor large proteins (τ_(iso)>23 ns; FIG. 31), but allowed one to use¹³C⁽¹⁾ polarization (Pervushin et al., J. Am. Chem. Soc. 120:6394-6400(1998), which is hereby incorporated by reference in its entirety) foracquiring central peaks (Kim et al., J. Am. Chem. Soc. 125:1385-1393(2003); Szyperski et al., J. Am. Chem. Soc. 118:8146-8147 (1996), whichare hereby incorporated by reference in their entirety) withoutcompromising on INEPT delays. (In aliphatic (4,3)D HCCH, central peakscan be derived from ¹³C polarization since INEPT is tuned for CH, CH₂,and CH₃ groups (Cavanagh et al., Protein NMR Spectroscopy: Principlesand Practice Academic Press: San Diego (1996), which is herebyincorporated by reference in its entirety). Aromatic spin systemscontain only CH and delays are tuned to ½ ¹J. Hence, ¹³C polarizationyields central peaks in aromatic non-TROSY (4,3)D HCCH only ifsensitivity of basic spectra is compromised.) These peaks provided(H)CCH information defining centers of peak pairs at Ω(¹³C⁽¹⁾)±Ω(¹H⁽¹⁾)in basic spectra.

L-GFT-TROSY (4,3)D HCCH (data set “I”) was recorded in 24 h witht_(rel)=1 s (t_(rel) ^(opt) for PfR13; Table 6) for 21 kDa protein HR41(FIG. 33; 25° C.; τ_(iso)˜11 ns; 95% peak detection yield), an NESGCtarget for which data collection is sensitivity limited. For sensitivitycomparison, L-GFT (“II”), GFT (“III”; t_(rel)=1.5 s with pre-saturationof water line), and L-GFT-TROSY with 13.5 ms ct delay (Pervushin et al.,J. Am. Chem. Soc. 120:6394-6400 (1998); Meissner et al., J. Magn. Reson.139:447-450 (1999), which are hereby incorporated by reference in theirentirety) (“IV”) were recorded. The relative intrinsic sensitivities of(4,3)D HCCH implementations (Table 6) are summarized in Table 7. TheSN_(t) values were determined for well resolved peaks and their ratioscalculated. Table 7 provides the average ratios with standarddeviations. The standard deviation for the comparison of L- versus non-Limplementation reflects the varying density of non-aromatic protonslocated around a given ¹H^(aromatic). The relative sensitivity for basicspectra was ˜2.5:3.8:2.1:1 (Table 7). Thus, at τ_(iso)˜11 ns, one hasthat (i) TROSY is ˜20% less sensitive (Theory predicts that at ct delaysof 4.5 and 13.5 ms, TROSY becomes more sensitive at τ_(iso)>˜23 ns andτ_(iso)>−8 ns, respectively (FIG. 31).) when also taking into accountthat ¹³C polarization yields central peaks in TROSY, (ii) L-optimizationincreases sensitivity by ˜20-60% (the variation is due to non-uniform ¹Hdensity), and (iii) t_(1,max)(¹³C⁽¹⁾)˜4.5 ms versus 13.5 ms (oftenrequired without GFT) increases TROSY sensitivity ˜2.5-fold. TABLE 6 GFTNMR Data Acquisition and Processing Parameters Indirect dimension:t_(max)(ms); Complex points; Total Peak Digital Meas. Detection (4,3)DHCCH Resolution t_(rel) Time Yield Experiment Protein [Hz/point]^(a) [s][h] [%]^(b) L-GFT-TROSY HR41 ω₁(¹³C; ¹³C, ¹H): 1.0 23.3 94 (92) (“I”)4.5; 30; 27 (2T = 4.5 ms) ω₂(¹³C): 4.5; 20; 70 L-GFT HR41 ω₁(¹³C; ¹³C,¹H): 1.0 17.5 95 (97) (“II”) 4.5; 30; 27 ω₂(¹³C): 4.5; 20; 70 GFT HR41ω₁(¹³C; ¹³C, ¹H): 1.5 17.5 88 (92) (“III”) 4.5; 30; 27 ω₂(¹³C): 4.5; 27;97 L-GFT-TROSY HR41 ω₁(¹³C; ¹³C, ¹H): 1.0 35.4 73 (70) (“IV”) 13.5; 90;27 (2T = 13.5 ms) ω₂(¹³C): 4.5; 20; 70 “previous” GFT HR41 ω₁(¹³C; ¹³C,¹H): 1.5  11.7^(d) 78^(d) (“V”)^(c) 4.5; 30; 27 ω₂(¹³C): 4.5; 27; 97 GFTMaR11 ω₁(¹³C; ¹³C, ¹H): 0.3  0.4 87 (89) 4.5; 21; 19 ω₂(¹³C): 4.5; 16;59 L-GFT MaR11 ω₁(¹³C; ¹³C, ¹H): 0.3  0.4  91 (100) 4.5; 21; 19 ω₂(¹³C):4.5; 16; 59^(a)direct dimension, ω₃(¹H): 57; 512; 9^(b)basic subspectra (central peak subspectrum)^(c)Shen et al., J. Am. Chem. Soc. 127: 9085-9099 (2005); Liu et al.,Proc. Natl. Acad. Sci. USA 102: 10487-10492 (2005), which are herebyincorporated by reference in their entirety^(d)only basic spectra were recorded

TABLE 7 Relative Sensitivity of Basic Spectra for (4,3)D HCCHImplementations SN_(t) ratio (basic spectra) SN_(t) ratio(centralΩ(¹³C) + Ω(¹H) Ω(¹³C) − Ω(¹H) peak spectra) Protein Comparison(range)^(a) (range)^(a) Ω(¹³C) (range)^(a) HR41 L-GFT (“II”) 1.6 ± 0.21.5 ± 0.2 6.5 ± 1.5 versus (1.1-2.2) (1.1-2.3)   (3-9.5) L-GFT-TROSY(“I”) (2T = 4.5 ms) L-GFT (“II”) 1.7 ± 0.3 1.8 ± 0.3 1.9 ± 0.4 versus(1.2-2.4) (1.1-2.8) (1.3-3.3) GFT (“III”) L-GFT-TROSY (“I”) 2.6 ± 0.82.5 ± 0.7 2.5 ± 0.7 (2T = 4.5 ms) (1.2-4.9) (1.5-4.8) (0.7-4.1) versusL-GFT-TROSY(“IV”) (2T = 13.5 ms) L-GFT(“II”) 3.0 ± 0.7 2.9 ± 0.6 versus(1.4-4.4) (1.5-4.9) “previous” GFT (“V”)^(b) MaR11 L-GFT 1.3 ± 0.2 1.3 ±0.2 1.4 ± 0.3 (FIG. 34) versus (1.0-1.9) (1.0-1.7) (1.0-2.0) GFT^(a)The minimum and maximum ratios of SN_(t) values are indicated.^(b)Shen et al., J. Am. Chem. Soc. 127: 9085-9099 (2005); Liu et al.,Proc. Natl. Acad. Sci. USA 102: 10487-10492 (2005), which are herebyincorporated by reference in their entirety

For GFT (4,3)D HCCH and L-GFT (4,3)D HCCH, two-thirds of the totalmeasurement time is invested for acquiring basic spectra, while onethird is required for central peak acquisition (by omitting the ¹Hchemical shift evolution). In TROSY congeners, the entire measurementtime is utilized for recording both basic and central peak subspectrasimultaneously, with the latter being derived from ¹³C steady-statepolarization (FIG. 33; Szyperski et al., Proc. Natl. Acad. Sci. USA99:8009-8014 (2002); Szyperski et al., J. Am. Chem. Soc. 118:8146-8147(1996), which are hereby incorporated by reference in their entirety).Hence, the SN_(t) values measured in the L-GFT-TROSY experiments can bemultiplied with √1.5=1.22 in order to also consider the need to acquirethe central peak subspectrum. Then, one has at τ_(iso)˜11 ns that TROSY(4.5 ms ct delay) is only ˜20% less sensitive than the non-TROSYcongener, and one would expect that TROSY becomes more sensitive atτ_(iso)˜15-20 ns (see FIG. 31).

Notably, the new L-GFT (4,3)D HCCH experiment (FIG. 32) was ˜3 timesmore sensitive than a hitherto used scheme (Shen et al., J. Am. Chem.Soc. 127:9085-9099 (2005); Liu et al., Proc. Natl. Acad. Sci. U.S.A.102:10487-10492 (2005), which are hereby incorporated by reference intheir entirety) (see grey entries in Table 7).

HR41 contains 6 Phe, 6 Tyr and 6 Trp, and nearly complete aromaticresonance assignment (Liu et al., J. Biomol. NMR 32:261-261 (2005),which is hereby incorporated by reference in its entirety) enabledhigh-quality NMR structure determination (Shen et al., J. Am. Chem. Soc.127:9085-9099 (2005); Liu et al., Proc. Natl. Acad. Sci. USA102:10487-10492 (2005), which are hereby incorporated by reference intheir entirety). Correlation of ¹³C^(γ) and Tyr ³C^(ζ) shifts with,respectively, ¹³C^(δ)/¹H^(δ) and Tyr ¹³C^(ε)/¹H^(ε) shifts supportedassignment of slowly flipping rings; the same C^(γ)/C^(ζ) shifts weredetected on CH^(δ/ε)-moieties belonging to an immobilized ring (FIG.33).

Nearly complete analysis of ¹H-linewidths was afforded with (4,3)D HCCH(Tables 8 and 9), which was important to explore flipping of all ringsin the protein. Comprehensive investigation of aromatic ring flippingrequires (i) resonance assignment and structure determination, (ii)measurement of (all) ¹H^(aromatic)-linewidths to identify rings forwhich a more detailed spectroscopic characterization of flippingkinetics is attractive (Wüthrich, NMR of proteins and Nucleic AcidsWiley: New York (1986); Wagner, Q. Rev. Biophys. 16:1-57 (1983);Skalicky et al., J. Am. Chem. Soc. 123:388-397 (2001), which are herebyincorporated by reference in their entirety), (iii) measurement offlipping rate constants, k_(flip), and (iv) determination of activationparameters. TABLE 8 ¹H^(aromatic) Line-Widths of HR41 at 25° C. from 2D[¹³C, ¹H] TROSY and (4,3)D HCCH ¹H linewidth [Hz] Residue Atom 2D [¹³C,¹H] L-GFT No. Residue Type TROSY (4,3)D HCCH Average 28 Trp H^(δ1) 32 —32 28 Trp H^(ε3) 42 40 41 28 Trp H^(η2) 40 41 41 28 Trp H^(ζ2) 38 — 3828 Trp H^(ζ3) — 42 42 36 Tyr H^(δ) — 21 21 36 Tyr H^(ε) — 21 21 42 TyrH^(δ) — 35 35 42 Tyr H^(ε) — 32 32 53 Trp H^(δ1) 35 — 35 53 Trp H^(η2)43 41 42 53 Trp H^(ζ2) — 35 35 53 Trp H^(ζ3) — 39 39 54 Phe H^(ε) 52 —52 54 Phe H^(ζ) 44 — 44 65 Trp H^(δ1) — <37^(a ) <37^(a ) 65 Trp H^(η2)— 39 39 65 Trp H^(ζ2) 38 34 36 66 Phe H^(δ) — 25 25 66 Phe H^(ε) 27 2425 66 Phe H^(ζ) 25 26 26 70 Trp H^(δ1) 33 39 36 70 Trp H^(ε3) — 34 34 70Trp H^(η2) — 42 42 70 Trp H^(ζ2) — 33 33 70 Trp H^(ζ3) — <36^(a )<36^(a ) 71 Tyr H^(δ) — <29^(a ) <29^(a ) 71 Tyr H^(ε) — <33^(a )<33^(a ) 78 Tyr H^(ε) — <35^(a ) <35^(a ) 80 Phe H^(δ) — 32 32 80 PheH^(ε) 41 41 41 80 Phe H^(ζ) 40 — 40 84 Phe H^(δ) 39 35 37 84 Phe H^(ε)44 42 43 84 Phe H^(ζ) 44 45 45 90 Tyr H^(δ1) 45 34 39 90 Tyr H^(δ2) — 3636 90 Tyr H^(ε1) — 32 32 90 Tyr H^(ε2) 40 38 39 110 Tyr H^(δ) 31 27 29110 Tyr H^(ε) — 27 27 121 Phe H^(δ) — <42^(a ) <42^(a ) 121 Phe H^(ε) —<42^(a ) <42^(a ) 121 Phe H^(ζ) 39 — 39 125 Trp H^(δ1) 34 35 35 125 TrpH^(η2) — <41^(a ) <41^(a ) 125 Trp H^(ζ2) — <39^(a ) <39^(a ) 132 PheH^(δ) 36 35 35 132 Phe H^(ε) 37 38 38 132 Phe H^(ζ) 39 — 39 145 TrpH^(δ1) 37 36 37 145 Trp H^(ε3) 51 — 51 145 Trp H^(η3) — <36^(a )<36^(a ) 145 Trp H^(ζ2) 43 44 43 145 Trp H^(ζ3) — <48^(a ) <48^(a )Completeness   42%   71%   85%^(a)Upper limit only due to spectral overlap.

TABLE 9 Average ¹H^(aromatic)-Linewidths of HR41 at 25° C. Proton type¹H-linewidths [Hz] All 36 ± 7 Phe (H^(δ)) 32 ± 5 Phe (H^(ε), H^(ζ)) 39 ±8 Trp (H^(δ1), H^(ζ2)) 36 ± 3 Trp (H^(ε3), H^(ζ3), H^(η2)) 42 ± 4 Tyr(H^(δ), H^(ε))^(a) 28 ± 6 Tyr 90 (H^(δ), H^(ε)) 37 ± 3^(a)Excluding Tyr 90.

For large proteins, measurement of ¹H^(aromatic)-linewidths (which canprovide estimates and/or bounds for flipping rates (Wüthrich, NMR ofProteins and Nucleic Acids Wiley: New York (1986); Wagner, Q. Rev.Biophys. 16:1-57 (1983); Skalicky et al., J. Am. Chem. Soc. 123:388-397(2001), which are hereby incorporated by reference in their entirety) inct 2D [¹³C,¹H]-HSQC/TROSY can be hampered by spectral overlap and, thus,use of higher-dimensional NMR techniques is required. For 21 kDa HR41,only 42% of the linewidths could be obtained in 2D NMR. In contrast,combining ct 2D [¹³C,¹H]-TROSY with (4,3)D HCCH (which allowed one toobtain 71% of the linewidths) yielded a largely complete (85%) analysis(Table 8).

In the slow exchange limit, excess line broadening, ΔΔν, provides anestimate for the rate constant (Skalicky et al., J. Am. Chem. Soc.123:388-397 (2001), which is hereby incorporated by reference in itsentirety). Comparison of the linewidths measured for Tyr 90 with thoseregistered for the other aromatic protons (Table 9) thus allows one toderive a bound for the flipping rate constant of Tyr 90. With ΔΔν<˜5 Hz,one obtains k_(flip)<˜ΔΔν˜15 s⁻¹. Consistently, neglecting a (small)contribution from dipolar interaction, one obtains from the ratio of¹H^(δ1)-¹H^(δ2) cross peak and diagonal peak volume ratio in¹³C^(aromatic)-resolved [¹H,¹H]-NOESY (Shen et al., J. Am. Chem. Soc.127:9085-9099 (2005); Liu et al., Proc. Natl. Acad. Sci. U.S.A.102:10487-10492 (2005), which are hereby incorporated by reference intheir entirety) that k_(flip)˜0.3 s⁻¹.

From ¹³C-resolved [¹H,¹H]-NOESY (Cavanagh et al., Protein NMRSpectroscopy: Principles and Practice Academic Press: San Diego (1996),which is hereby incorporated by reference in its entirety), k_(flip)(Tyr90)˜0.3 s⁻¹ reflected a slow motional mode on the seconds time scale,proving the absence of faster large amplitude motions enabling ringflipping. This indicated remarkable rigidity of the sub-structure inwhich the ring was embedded. Tyr 90 is conserved amongubiquitin-conjugating enzymes E2 (to which HR41 belongs as inferred fromstructure (Liu et al., Proc. Natl. Acad. Sci. U.S.A. 102:10487-10492(2005), which is hereby incorporated by reference in its entirety)) andis located in spatial proximity to the interface between E2 and theubiquitin-protein ligase E3 (Huang et al., Science 286:1321-1326 (1999);VanDemark et al., Curr. Opin. Struct. Biol. 12:822-830 (2002), which arehereby incorporated by reference in their entirety). Hence, the rigidityand/or the slow motional mode might be important for E2-E3 dimerizationand, thus, for cellular protein degradation.

L-optimization for rapid data acquisition (FIG. 30) was also exemplifiedfor 13 kDa protein MaR11 (Liu et al., Proc. Natl. Acad. Sci. USA102:10487-10492 (2005), which is hereby incorporated by reference in itsentirety) (1 mM; Table 6; FIG. 34), an NESG target for which datacollection is sampling limited (With t_(rel)=0.3 s, the minimalmeasurement times of L-4D HCCH and L-GFT (4,2)D HCCH (Atreya et al.,Proc. Natl. Acad. Sci. USA 101:9642-9647 (2004), which is herebyincorporated by reference in its entirety) were 4.9 hrs and 3 min,respectively.): L-GFT (4,3)D HCCH was acquired with t_(rel)=0.3 s in 25min (Table 6; 94% peak detection yield).

Overall, for proteins up to ˜25 kDa, PFG-PEP ct L-2D [¹³C,¹H]-TROSY andL-GFT (4,3)D HCCH were most sensitive, while the TROSY congener wasattractive for large proteins and slowly flipping (nearly stalled)rings, which are unique reporters of slow protein dynamics (Wüthrich,NMR of proteins and Nucleic Acids Wiley: New York, (1986); Wagner, Q.Rev. Biophys. 16:1-57 (1983); Skalicky et al., J. Am. Chem. Soc.123:388-397 (2001), which are hereby incorporated by reference in theirentirety). Aromatic L-optimization includes “flip-back” of ¹H₂Opolarization (Grzesiek et al., J. Am. Chem. Soc. 115:12593-12594 (1993),which is hereby incorporated by reference in its entirety), which isimportant for systems >100 kDa (Wider, Method Enzymol. 394:382-398(2005), which is hereby incorporated by reference in its entirety). Itis thus expected that L-GFT(-TROSY) (4,3)D HCCH NMR will play a key rolefor high-quality structure determination of large (membrane) (Atreya etal., J. Am. Chem. Soc. 127:4554-4555 (2005), which is herebyincorporated by reference in its entirety) proteins and for studying thequite unexplored (functional) dynamics of their molecular cores.

Example 9 GFT NOESY-Based Protocol—NMR Sample Characterization

NMR experiments were performed on a 600 MHz spectrometer equipped with acryogenic probe (Styles et al., Magn. Reson. 60:397-404 (1994), which ishereby incorporated by reference in its entirety) for the 103-residuetarget protein YqfB of the Northeast Structural Genomics consortium(NESG; NESG ID: ET99). To ensure that results were representative formedium-sized proteins, NMR experiments were conducted with a 1 mMprotein solution at ambient temperature 25° C.

Uniformly (U) ¹³C,¹⁵N-labeled YqfB was produced as described in Yee etal., Proc. Natl. Acad. Sci. USA 99:1825-1830 (2002), which is herebyincorporated by reference in its entirety. The protein contained a22-residue N-terminal tag with sequence MGTSHHHHHHSSGRENLYFQGH (SEQ IDNO:1) in order to facilitate purification. Thus, the polypeptideexpressed for NMR structural studies had a molecular weight of 15.3 kDaand 14.5 kDa, respectively, with and without ¹³C/¹⁵N double labeling.U-¹³C,¹⁵N YqfB was concentrated to an ˜1 mM solution in 90% H₂O/10% ²H₂O(25 mM Na phosphate, pH=6.5, 400 mM NaCl, 1 mM DTT, 20 mM ZnCl₂, 0.01%NaN₃). The approximate isotropic overall rotational correlation time,τ_(r), of the protein was determined (at a ¹H resonance frequency of 600MHz) from ¹⁵N T₁/T_(1ρ) nuclear spin relaxation time ratios, as wasdescribed in Szyperski et al., Proc. Natl. Acad. Sci. USA 99:8009-8014(2002), which is hereby incorporated by reference in its entirety. Inagreement with a molecular weight of 15.5 kDa for U-¹³C,¹⁵N YqfB,τ_(r)˜7.7 ns was obtained. This demonstrated that the protein wasmonomeric in solution.

Example 10 GFT NOESY-Based Protocol—Implementation of GFT (4,3)D [HC^(ali)/HN]-NOESY-[CH^(ali)/NH]

The chemical shift measurements and NOE transfers taking place insimultaneous GFT (4,3)D [HC ^(ali)/HN]-NOESY-[CH^(ali)/NH] are shown inFIG. 35. Chemical shift doublets were registered in the GFT dimension atω₁:Ω(¹H)±κ·Ω(X) [X=¹⁵N,¹³C^(aliphatic)], where κ represents a factor forscaling the projected chemical shift evolution (Szyperski et al., J. Am.Chem. Soc. 115:9307-9308 (1993), which is hereby incorporated byreference in its entirety). Proton polarization was transferred to theattached heteronucleus, frequency labeled with Ω(X), transferred back tothe proton and frequency labeled with Ω(¹H). The latter shift wasdetected in quadrature (Cavanagh et al., Protein NMR SpectroscopyAcademic Press: San Diego (1996), which is hereby incorporated byreference in its entirety). Hence, with κ=0.5, one has that G-matrixtransformation yields two subspectra with peaks located either atΩ(¹H)+0.5·Ω(X) or Ω(¹H)−0.5·Ω(X) [i.e., the peak separation matchesΩ(X)]. After NOE mixing, the polarization was transferred to the secondheteronucleus for frequency labelling, and then transferred back to theattached proton for signal detection. As a result, polarizationtransfers and chemical shift measurements of 4D ¹⁵N/¹⁵N-,¹³C^(alipahtic)/¹⁵N- and ¹³C^(aliphatic)/¹³C^(aliphatic)-resolved[¹H,¹H]-NOESY occurred simultaneously. For detection of central peakslocated at ω₁:Ω(¹H), frequency labelling on the first heteronucleus wasnot required and hence the additional simultaneous heteronuclearpolarization transfer was omitted (see below). It is advantageous todetect central peaks in conjunction with NOEs on aromatic protons. Inthis experiment, the polarization transfers of 3D ¹⁵N-, ¹³C^(aliphatic)and ¹³C^(aromatic)-resolved [¹H,¹H]-NOESY occurred simultaneously. Foruniformity of nomenclature, this experiment here was named as “3D[H]-NOESY-[CH^(ali)/CH^(aro)/NH]”, where chemical shifts are measuredfor nuclei indicated in brackets.

The r.f. pulse scheme for the detection of shift doublets (FIG. 36(a))was derived from simultaneous 3D ¹⁵N,¹³C^(aliphatic)-resolved[¹H,¹H]-NOESY (Xia et al., J. Biomol. NMR 27:193-203 (2003), which ishereby incorporated by reference in its entirety) by inserting anadditional simultaneous [¹H,¹³C]/[¹H,¹⁵N]-HSQC module (Cavanagh et al.,Protein NMR Spectroscopy Academic Press: San Diego (1996), which ishereby incorporated by reference in its entirety) before NOE mixing. Tominimize signal losses arising from T₂(¹H) relaxation, ¹H chemical shiftevolution was implemented in a semiconstant time manner (Cavanagh etal., Protein NMR Spectroscopy Academic Press: San Diego (1996), which ishereby incorporated by reference in its entirety) during the reverseINEPT (Cavanagh et al., Protein NMR Spectroscopy Academic Press: SanDiego (1996), which is hereby incorporated by reference in itsentirety). To maximize intensity of ¹H^(aliphatic)—¹H^(aliphatic) NOEs,INEPT delays were tuned to ½¹J_(CHalphatic). Moreover, ¹³C and ¹⁵Nchemical shift evolution in the GFT dimension was scaled (Szyperski etal., J. Am. Chem. Soc. 115:9307-9308 (1993), which is herebyincorporated by reference in its entirety) down with κ=0.5, limitingt_(1,max)(¹³C/¹⁵N) to ˜8 ms. This reduced the sensitivity loss arisingfrom both transverse T₂(¹³C/¹⁵N) relaxation and passive aliphaticone-bond ¹³C—¹³C scalar couplings (˜35 Hz). Likewise, starting from thescheme of 3D ¹⁵N,¹³C^(aliphatic)-resolved [¹H,¹H]-NOESY (Xia et al., J.Biomol. NMR 27:193-203 (2003), which is hereby incorporated by referencein its entirety), 3D [H]-NOESY-[CH^(ali)/CH^(aro)/NH] was implementedfor acquisition of central peaks and NOEs detected on aromatic protons.For completeness, the r.f. pulse scheme is shown in FIG. 36(b).

Example 11 GFT NOESY-Based Protocol—NMR Data Acquisition and Processing

NMR spectra for resonance assignment (Table 10) and structuredetermination (Tables 10 and 11) of YqfB were recorded at 25° C. on aVarian INOVA 600 spectrometer equipped with a cryogenic ¹H{¹³C,¹⁵N}triple resonance probe, and processed using the program PROSA (Güntertet al., J. Biomol. NMR 2:619-629 (1992), which is hereby incorporated byreference in its entirety). The cryogenic probe used delivered asignal-to-noise ratio of 4,500:1 for the standard ethylbenzene sample(which is about four times larger than what is measured for theconventional ¹H{¹³C,¹⁵N} probe). A detailed comparison pursued for 17kDa NESG target protein YgdK dissolved in a 90% H₂O/10% ²H₂O buffer (pH6.5) containing 100 mM NaCl revealed that the cryogenic probe increased(on average) sensitivity by a factor of ˜3 for double/triple resonanceexperiments and NOESY. Due to higher salt content (400 mM NaCl), thegain in sensitivity for the YqfB measurements was lowered to a factor of˜2. Hence, the NMR measurement times reported herein (Table 11) wouldhave been about four times longer if conducted with a conventionalprobe. TABLE 10 Through-bond GFT NMR Experiments for ResonanceAssignment of Protein YqfB Minimal Linear combinations measurement timeof chemical shifts (hrs)^(b) Experiment Polarization transferpathway^(a) observed along ω₁ GFT non-GFT (4,3)D HNNC ^(αβ) C ^(α)¹HN_(i)→¹⁵N_(i) ¹³C^(α) _(i/i−1)→ ¹³C^(αβ) _(i/i−1)→ ¹³C^(α) _(i/i−1)→¹⁵N_(i)→ ¹HN_(i) Ω(¹³C^(α) _(i/i−1)) ± Ω(¹³C^(α) _(i/i−1)) 2.5 38 (t₁)(t₁) (t₂) (t₃) Ω(¹³C^(α) _(i/i−1)) ± Ω(¹³C^(β) _(i/i−1)) (4,3)D ¹H^(αβ)_(i−1)→ ¹³C^(αβ) _(i−1)→ ¹³C^(α) _(i−1)→ ¹³C′_(i−1)→ ¹⁵N_(i)→ ¹HN_(i)Ω(¹³C^(α) _(i−1)) ± Ω(¹³C^(α) _(i−1)) 2.5 38 C ^(αβ) C ^(α)(CO)NHN (t₁)(t₁) (t₂) (t₃) Ω(¹³C^(α) _(i−1)) ± Ω(¹³C^(β) _(i−1)) (5,2)D ¹H^(α)_(i−1)→ ¹³C^(α) _(i−1)→ ¹³C′_(i−1)→ ¹⁵N_(i)→ ¹HN_(i) Ω(¹⁵N_(i)) ±Ω(¹³C′_(i−1)) 0.45^(c) 102 HACACONHN (t₁) (t₁) (t₁) (t₁) (t₂) ±Ω(¹³C^(α)_(i−1)) ± Ω(¹H^(α) _(i−1)) (4,3)D HCCH ¹H⁽¹⁾→ ¹³C⁽¹⁾→ ¹³C⁽²⁾→ ¹H⁽²⁾Ω(¹³C⁽¹⁾) ± Ω(¹H⁽¹⁾) 1.9/0.63^(c) 31/2.2 aliphatic/aromatic (t₁) (t₁)(t₂) (t₃) Ω(¹³C⁽²⁾) ± Ω(¹H⁽²⁾)^(a)i−1 and i indicate two neighboring amino acid residues along thepolypeptide chain. t₁, t₂, and t₃ denote the indirect evolution periodsused for frequency labeling of the respective spins.^(b)The minimal measurement times for GFT and parent (“non-GFT”)experiments were calculated by choosing the acquisition parameters ofTable 11, and assuming that a single scan per “free induction decay”(FID) is recorded. Spectral widths: ¹³C^(α): 3,000 Hz; ¹³C^(αβ): 9,000Hz; ¹³C^(aliphatic): 9,000 Hz; ¹³C^(aromatic): 4,500 Hz;# ¹H^(aromatic): 1,500 Hz; ¹H^(aliphatic): 6,000 Hz, ¹H^(α): 1,800 Hz;¹⁵N: 1,600 Hz; ¹³C′: 1,400 Hz. Delay between start of FID acquisitions(“recycle delays”): 0.55 s for (4,3)D HNNC ^(αβ) C ^(α) and (4,3)D C^(αβ) C ^(α)(CO)NHN; # 0.95 s for (5,2)D HACACONHN, 0.39 s for (4,3)DHCCH (aliphatic) and 0.47 s for (4,3)D HCCH (aromatic). For experimentsencoding K+1 shifts in the “GFT dimension”, the spectral width alongthis dimension (ω₁) is: (Kim et al., J. Am. Chem. Soc. 125: 1385-1393(2003), which is hereby incorporated by reference in its entirety), #Σ^(K) _(j=0)SW_(j). The measurement times given includes the timerequired for recording both basic and central peak spectra. Note, thatthe third order central peak spectrum of (5,2)D HACACONHN is equivalentto 2D[¹⁵N,¹H]HSQC.^(c)Assuming that central peak spectra are acquired by successiveomission of indirect evolution periods.

TABLE 11 Acquisition Parameters of NMR Experiments Indirect dimension:Measure- t_(max) (ms); Complex points; ment Experiment DigitalResolution (Hz/Pt)^(a) time (hrs) (4,3)D HNNC^(αβ)C^(α) ω₁(¹³C^(α);¹³C^(αβ)): 6.4; 78; 23 5.0 ω₂(¹⁵N): 15.6; 26; 25 (4,3)DC^(αβ)C^(α)(CO)NHN ω₁(¹³C^(α); ¹³C^(αβ)): 6.4; 78; 23 5.0 ω₂(¹⁵N): 15.6;26; 25 (5,2)D HACACONHN ω₁(¹⁵N; ¹³C′, ¹³C^(α), ¹H^(α)): 6.3; 1.5^(b) 48;14 (4,3)D HCCH (aliphatic) ω₁(¹³C; ¹H): 6.3; 95; 29 4.0^(c) ω₂(¹³C):3.6; 16; 70 (4,3)D HCCH (aromatic) ω₁(¹³C; ¹H): 4.0; 25; 23 1.4^(d)ω₂(¹³C): 3.8; 16; 62 3D [H]-NOESY- ω₁(¹H): 16; 128; 15 9.1[CH^(ali)/CH^(aro)/NH] ω₂(¹³C): 6.4; 28; 67 ω₂(¹⁵N): 17; 28; 25 Shiftdoublets of ω₁(¹H): 16; 200; 24.4 30/60^(e) (4,3)D [HC^(ali)/HN]-ω₁(¹³C/¹⁵N): 8; 200; 24.4 NOESY-[CH^(ali)/NH] (“data ω₂(¹³C): 6.4; 28;67 sets I/II”) ω₂(¹⁵N): 16.5; 28; 25^(a)Direct dimension: ω₃(¹H): 64; 512; 8. All spectra were recorded with2 scans per FID unless indicated differently in a separate footnote. For“recycle delays” see footnote ‘b’ of Table 10.^(b)Includes 5 minutes to record a 2D [¹⁵N,¹H]-HSQC, that is, thirdorder central peak, spectrum with t_(max)(¹⁵N) = 24 ms and a single scanper FID. Other spectra were acquired with 4 scans per FID.^(c)Includes 12 minutes to record a 2D constant time [¹³C,¹H] HSQC⁷ witht_(max)(¹³C) = 28 ms.^(d)Includes 10 minutes to record a 2D constant time [¹³C,¹H] HSQC⁷ witht_(max)(¹³C) = 18 ms with 4 scans per FID.^(e)Data sets I and II were recorded with 2 and 4 scans per FID,respectively. Hence, the minimal measurement time is 15 hours.

GFT NMR data for resonance assignment were acquired in 16.9 hours (Table11), while NOESY data were recorded with a total measurement time of 39hours; (4,3)D [HC ^(ali)/HN]-NOESY-[CH^(ali)/NH] shift doublets wereacquired in 30 hours (hereafter referred to as “data set I”) using thepulse scheme of FIG. 36(a) and central peaks were obtained from 3D[H]-NOESY-[CH^(ali)/CH^(aro)/NH] (FIG. 36(b)) acquired in 9.1 hours(Table 11). For comparison, a second data set (“data set II”) comprisingthe shift doublets was acquired with twice the measurement time (60hours; Table 11).

Example 12 GFT NOESY-Based Protocol—Analysis of Through-Bond GFT NMRCorrelation Spectra for Resonance Assignment

As a salient feature, GFT NMR affords linear combinations of shiftsencoded in chemical shift multiplets (Table 10), and G-matrixtransformation warrants editing of the multiplet components intodifferent subspectra (Atreya et al., Proc. Natl. Acad. Sci. USA101:9642-9647 (2004); Kim et al., J. Am. Chem. Soc. 125:1385-1393(2003); Kim et al., J. Biomol. NMR 28:117-130 (2004), which are herebyincorporated by reference in their entirety). Hence, the number of peaksper subspectrum does not increase when increasing the number of jointlysampled indirect chemical shift evolution periods. Concomitantly, thepeak dispersion (and thus spectral resolution) increases when comparedwith conventional congeners (Cavanagh et al., Protein NMR SpectroscopyAcademic Press: San Diego (1996), which is hereby incorporated byreference in its entirety) of the same dimensionality (Atreya et al.,Proc. Natl. Acad. Sci. USA 101:9642-9647 (2004), which is herebyincorporated by reference in its entirety). Hence, the analysis of GFTNMR subspectra is quite generally less challenging than the analysis ofthe conventional congeners. For the present invention, the program XEASY(Bartels, J. Biomol. NMR 6:1-10 (1995), which is hereby incorporated byreference in its entirety) was used for data analysis. Importantly,XEASY can handle linear combinations of shifts by expanding chemicalshift lists accordingly. This option was originally introduced foranalysis of RD NMR spectra (Szyperski et al., J. Am. Chem. Soc.115:9307-9308 (1993); Szyperski et al., J. Magn. Reson. B105:188-191(1994); Brutscher et al., J. Magn. Reson. B105:77-82 (1994); Szyperskiet al., J. Magn. Reson. B108:197-203 (1995); Szyperski et al., J. Am.Chem. Soc. 118:8146-8147 (1996); Szyperski et al., J. Biomol. NMR11:387-405 (1998); Szyperski et al., Proc. Natl. Acad. Sci. USA99:8009-8014 (2002); Bartels, J. Biomol. NMR 6:1-10 (1995), which arehereby incorporated by reference in their entirety) and allows one toassign linear combinations of shifts to peak positions. The chemicalshifts are readily obtained from peak positions encoding the linearcombinations by use of a simple linear least-squares fit (Kim et al., J.Am. Chem. Soc. 125:1385-1393 (2003), which is hereby incorporated byreference in its entirety). Visual inspection of matching linearcombinations of shifts, either within one spectrum or between severalspectra, was accomplished as for conventional spectra by use of XEASY.Peak picking was achieved by (i) generating peak lists from averagedshifts taken from the BioMagResBank or from shifts that were obtained atan earlier stage of the resonance assignment protocol, and (ii) manualadjustment of these lists.

Example 13 GFT NOESY-Based Protocol—Analysis of NOESY Data

NOESY spectra were analyzed using the program XEASY (Bartels, J. Biomol.NMR 6:1-10 (1995), which is hereby incorporated by reference in itsentirety). 3D [H]-NOESY-[CH^(ali)/CH^(aro)/NH] comprises the centralpeaks of (4,3)D [HC ^(ali)/HN]-NOESY-[CH^(ali)/NH] (FIG. 35) and wasanalyzed as described in the following. First, based on backbone and¹³C^(β) chemical shifts, the location of the regular secondary structureelements of YqfB was identified (Wishart et al., Biochemistry31:1647-1650 (1994), which is hereby incorporated by reference in itsentirety). Subsequently, an initial 3D NOESY peak list was generatedthat contained the expected intraresidue, sequential and medium rangeNOE peak positions. After manual adjustment of peak positions andidentification of other, primarily long-range NOE peaks, all peaks wereintegrated. To confirm assignments of overlapped peaks, line shapes werecompared visually. The final 3D [H]-NOESY-[CH^(ali)/CH^(aro)/NH] peaklist, which yielded a high-quality structure of protein YqfB (PDB ID1TE7; see Example 19), was used as a reference peak list to evaluate theimpact of (4,3)D [HC ^(ali)/HN]-NOESY-[CH^(ali)/NH]. First, it wasdetermined how many peaks in 3D NOESY can be assigned based on chemicalshift data only [matching tolerances: 0.02 ppm for Ω(¹H); 0.2 ppm forΩ(¹⁵N) and Ω(¹³C)], that is, without reference to an (initial)structure. Second, the spectra comprising the doublets were analyzed asdescribed in the following. (i) The two subspectra containing the shiftdoublets were assigned in a bottom-up manner (Kim et al., J. Am. Chem.Soc. 125:1385-1393 (2003), which is hereby incorporated by reference inits entirety) starting from the 3D [H]-NOESY-[CH^(ali)/CH^(aro)/NH] peaklist; for each peak in 3D NOESY representing a central peak of (4,3)D[HC ^(ali)/HN]-NOESY-[CH^(ali)/NH], the corresponding shift doublet wasidentified and the additionally encoded heteronuclear chemical shift wasmeasured. It was then determined which peaks in 3D NOESY can be assignedunambiguously when having the additional, fourth chemical shift (withthe matching tolerances indicated above). (ii) The subspectra containingthe shift doublets were examined in order to identify “new” NOEs whichcould not be resolved and/or assigned in 3D[H]-NOESY-[CH^(ali)/CH^(aro)/NH], even with reference to a high-qualityNMR structure. (iii) The S/N ratios of a large number of peaks weremeasured in order to assess the relative sensitivity of shift doubletcompared to central peak detection. (iv) It was determined whichfraction of the NOEs detected and assigned in 3D NOESY was likewiseobserved in the subspectra containing the shift doublets. This yielded ashift doublet detection yield relative to the (more sensitive) centralpeak detection.

Example 14 GFT NOESY-Based Protocol—NMR Structure Calculations

Cross-peak volumes measured in 3D [H]-NOESY-[CH^(ali)/CH^(aro)/NH] wereconverted into ¹H—¹H upper distance limit constraints by using theprogram DYANA (Güntert et al., J. Mol. Biol. 273:283-298 (1997), whichis hereby incorporated by reference in its entirety). Cross peaksoverlapping in 3D [H]-NOESY-[CH^(ali)/CH^(aro)/NH], but resolved in theshift doublet spectra of (4,3)D [HC ^(ali)/HN]-NOESY-[CH^(ali)/NH], wereinterpreted conservatively and used to derive 5 Å distance limitconstraints. Residues of regular secondary structure elements wereinitially identified by use of the chemical shift index method (Wishartet al., Biochemistry 31:1647-1650 (1994), which is hereby incorporatedby reference in its entirety), and for polypeptide segments with threeor more such identified consecutive residues, φ and ψ backbone dihedralangle constraints were derived from the chemical shifts by use of theprogram TALOS (Cornilescu et al., J. Biomol. NMR 13:289-302 (1999),which is hereby incorporated by reference in its entirety). No hydrogenbond constraints were used. The final round of DYANA structurecalculations employing torsion angle dynamics was started with 100random conformers and 30,000 annealing steps, and the 20 structures withthe lowest DYANA target functions were selected to represent thesolution structure. Stereospecific assignments for calculating therefined reference structure were obtained using the FOUND and GLOMSAmodules of DYANA (Güntert et al., J. Mol. Biol. 273:283-298 (1997),which is hereby incorporated by reference in its entirety). TheRamachandran map statistics of NMR structures was evaluated using theprogram PROCHECK (Laskowski et al., J. Biomol. NMR 8:477-486 (1996),which is hereby incorporated by reference in its entirety).

Example 15 GFT NOESY-Based Protocol—Automated NOE Assignment andStructure Calculation with CYANA

Calculations with the program CYANA (Herrmann et al., J. Mol. Biol.319:209-227 (2002), which is hereby incorporated by reference in itsentirety) were performed for automated NOE assignment and structurecalculation using the standard protocol with 7 cycles. (For the presentinvention, an evaluation using the program CYANA was best suited. Thiswas because, for YqfB, all intraresidue, sequential and medium-rangeNOEs were assigned by predicting NOESY peak lists from chemical shiftdata and considering information on secondary structure elements. Hence,a top-down algorithm appeared to be the natural choice to complement thechemical shift based assignment protocol.) Matching tolerances forchemical shifts were set to 0.02 ppm for Ω(¹H) and to 0.2 ppm for Ω(¹³C)and Ω(¹⁵N). CYANA structure calculations were started with 100 randomconformers and 30,000 annealing steps. The 20 conformers with lowesttarget function value were selected for the next cycle of NOEassignment. In routine applications, automatically obtained NOE peakassignments were confirmed by visual inspection of spectra. To assessthe impact of network anchoring (Herrmann et al., J. Mol. Biol.319:209-227 (2002), which is hereby incorporated by reference in itsentirety) in a first cycle of a CYANA calculation, the entire 3D NOESYreference peak lists were provided as input and combined with ¹H—¹Hupper distance limit constraints derived from intraresidue, sequential,and medium-range NOEs (which were assigned as described in Example 13above) and chemical shift derived (Cornilescu et al., J. Biomol. NMR13:289-302 (1999), which is hereby incorporated by reference in itsentirety) dihedral angle constraints. In addition, two CYANAcalculations (referred to as (1) and (2) below) were performed to assessthe impact of NOEs which could be assigned in (4,3)D [HC^(ali)/HN]-NOESY-[CH^(ali)/NH] using chemical shift data only. In thesecalculations, a peak list containing only the remaining, unassignedlong-range NOEs was provided as input. Specifically, calculations (1)and (2) were performed with the following input: (i) list of unassignedpeaks of 3D [H]-NOESY-[CH^(ali)/CH^(aro)/NH] reference peak list, (ii)TALOS dihedral angle constraint list which yielded the referencestructure of YqfB (1TE7; see Example 19), (iii) distance limitconstraints representing intraresidue, sequential and medium-range NOEs(see above), and (iv) distance constraints representing long-range NOEsthat were assigned in the 3D [H]-NOESY-[CH^(ali)/CH^(aro)/NH] referencepeak list based on chemical shifts and (1) the shift doublets registeredin the (4,3)D [HC ^(ali)/HN]-NOESY-[CH^(ali)/NH] subspectra of data setI (recorded in 30 hours), or (2) the shift doublet subspectra of dataset II (recorded in 60 hours).

Example 16 GFT NOESY-Based Protocol—Evaluation of NOE InformationContent with the Program QUEEN

The program QUEEN (Nabuurs et al., J. Am. Chem. Soc. 125:12026-12034(2003), which is hereby incorporated by reference in its entirety)affords quantitative evaluation of sets of NOEs using criteriaoriginally developed for information theory. This program was used toanalyze the information content of long-range NOEs assigned in (4,3)D[HC ^(ali)/HN]-NOESY-[CH^(ali)/NH] acquired with 3D[H]-NOESY-[CH^(ali)/CH^(aro)/NH] for central peak detection. For eachconstraint network, the total information content, I_(total) (seeequation 8 in Nabuurs et al., J. Am. Chem. Soc. 125:12026-12034 (2003),which is hereby incorporated by reference in its entirety), and for eachindividual constraint within a given network, the unique information,I_(uni) (equation 10 in Nabuurs et al., J. Am. Chem. Soc.125:12026-12034 (2003), which is hereby incorporated by reference in itsentirety), and the average information, I_(ave) (equation 11 in Nabuurset al., J. Am. Chem. Soc. 125:12026-12034 (2003), which is herebyincorporated by reference in its entirety), were calculated. Thelong-range upper distance constraint networks derived from the followingNOE peak lists were subject to such an analysis: (1) 3D[H]-NOESY-[CH^(ali)/CH^(aro)/NH] reference peak list, (2) listcomprising peaks assigned in 3D [H]-NOESY-[CH^(ali)/CH^(aro)/NH] basedon shift data only, (3) list comprising peaks assigned in 3D[H]-NOESY-[CH^(ali)/CH^(aro)/NH] based on shift data only but withreference to 4D information encoded in shift doublet data set I, and (4)same as (3) but with shift doublet data set II.

Example 17 GFT NOESY-Based Protocol—Resonance Assignment

Efficient analysis of NOESY spectra requires resonance assignments(Wüthrich, NMR of Proteins and Nucleic Acids Wiley: New York (1986),which is hereby incorporated by reference in its entirety). Inspectionof the 2D [¹⁵N,¹H] HSQC spectrum revealed that protein YqfB exhibited anoverall good ¹⁵N/¹H^(N) chemical shift dispersion. However, the centralregion of the spectrum was crowded, partly due to peaks arising from a22-residue tag added to facilitate purification. Such ¹⁵N/¹H^(N)chemical shift degeneracy posed a challenge for efficient backboneresonance assignment and made YqfB an attractive target for GFT NMRspectroscopy, which provides high dimensional spectral information(Atreya et al., Proc. Natl. Acad. Sci. USA 101:9642-9647 (2004); Kim etal., J. Am. Chem. Soc. 125:1385-1393 (2003); Kim et al., J. Biomol. NMR28:117-130 (2004), which are hereby incorporated by reference in theirentirety) to break shift degeneracy.

For obtaining (nearly) complete resonance assignments, a set of fivethrough-bond GFT NMR experiments (Table 10) was performed in 16.9 hours(Table 11): (4,3)D HNNC ^(αβ) C ^(α) and C ^(αβ) C ^(α)(CO)NHN forbackbone and ¹³C^(β) assignment (Atreya et al., Proc. Natl. Acad. Sci.USA 101:9642-9647 (2004), which is hereby incorporated by reference inits entirety), (5,2)D HACACONHN (Kim et al., J. Am. Chem. Soc.125:1385-1393 (2003), which is hereby incorporated by reference in itsentirety) for ¹H^(α) assignment, and aliphatic/aromatic (4,3)D HCCH,derived from RD 3D HCCH (Szyperski et al., Proc. Natl. Acad. Sci. USA99:8009-8014 (2002), which is hereby incorporated by reference in itsentirety), for side chain spin system identification. FIG. 37illustrates the resulting GFT NMR based resonance assignment strategyfor protein YqfB. For backbone and ¹³C^(β) resonance assignment, jointanalysis of two subspectra of (4,3)D HNNC ^(αβ) C ^(α) and C ^(αβ) C^(α)(CO)NHN (Atreya et al., Proc. Natl. Acad. Sci. USA 101:9642-9647(2004), which is hereby incorporated by reference in its entirety)proceeded conceptually as for 3D HNNCACB/CBCA(CO)NHN (Cavanagh et al.,Protein NMR Spectroscopy Academic Press: San Diego (1996), which ishereby incorporated by reference in its entirety). The analysis of(5,2)D HACACONHN described previously (Kim et al., J. Am. Chem. Soc.125:1385-1393 (2003), which is hereby incorporated by reference in itsentirety) involved generating 15 2D peak lists from which >quintuples ofchemical shifts were calculated. For side chain assignment, analysis ofeach of the three subspectra of (4,3)D HCCH proceeded conceptually asfor conventional 3D H(C)CH (Cavanagh et al., Protein NMR SpectroscopyAcademic Press: San Diego (1996), which is hereby incorporated byreference in its entirety). First, (4,3)D HCCH and 3D H(C)CH wereindistinguishable in both the indirect carbon and direct protondimensions. Second, ω₁:Ω(¹³C)+Ω(¹H), ω₁:Ω(¹³C)−Ω(¹H) (chemical shiftdoublets) and ω₁:Ω(¹³C) (central peaks) were detected along the GFTdimension in the three subspectra of (4,3)D HCCH (Table 10), while Ω(¹H)was detected along ω₁ in 3D H(C)CH. Hence, spin system identification in(4,3)D HCCH can be visualized as “walking” into the side chains by useof (i) Ω(¹³C), (ii) Ω(¹³C+¹H), and (iii) Ω(¹³C—¹H).

Through-bond GFT NMR (Atreya et al., Proc. Natl. Acad. Sci. USA101:9642-9647 (2004); Kim et al., J. Am. Chem. Soc. 125:1385-1393(2003); Kim et al., J. Biomol. NMR 28:117-130 (2004), which are herebyincorporated by reference in their entirety) provided the spectralinformation of one 5D and four 4D conventional FT NMR spectra with highdigital resolution (Table 11; FIG. 37), yielding nearly completeresonance assignments (98% of backbone and 95% of the side chainchemical shifts; BMRB ID 6207) with investment of 16.9 hours ofinstrument time. Importantly, the availability of thehighest-dimensional spectral information ensured that data analysis was(i) robust with respect to occurrence of chemical shift degeneracies,(ii) highly reliable with respect to assignment yield and accuracy, and(iii) amenable to automated protocols due to increased peak dispersionand precision of shift measurements (Atreya et al., Methods Enzymol.394:78-108 (2005); Atreya et al., Proc. Natl. Acad. Sci. USA101:9642-9647 (2004); Kim et al., J. Am. Chem. Soc. 125:1385-1393(2003); Kim et al., J. Biomol. NMR 28:117-130 (2004), which are herebyincorporated by reference in their entirety). Analysis of the twobackbone experiments, (4,3)D HNNC ^(αβ) C ^(α)/C ^(αβ) C ^(α)(CO)NHN,greatly profited from (i) the intraresidue ¹³C^(α)—¹³C^(β) shiftcorrelations and (ii) the doubled dispersion manifested, for example, bypeaks encoding 2·Ω(¹³C^(α)) instead of (¹³C^(α)) (see FIG. S12 in Atreyaet al., Methods Enzymol. 394:78-108 (2005), which is hereby incorporatedby reference in its entirety). Moreover, it has been shown that 4Dinformation encoded in RD 3D HCCH enables efficient assignment of thealiphatic side chains of proteins with molecular weights up to at least˜18 kDa (Shen et al., J. Biomol. NMR 29:549-550 (2004), which is herebyincorporated by reference in its entirety). That finding was confirmedhere with the resonance assignment of YqfB using (4,3)D HCCH, the GFTNMR congener of RD 3D HCCH. Taken together, the through-bond GFT NMR(Atreya et al., Proc. Natl. Acad. Sci. USA 101:9642-9647 (2004); Kim etal., J. Am. Chem. Soc. 125:1385-1393 (2003); Kim et al., J. Biomol. NMR28:117-130 (2004), which are hereby incorporated by reference in theirentirety)-based resonance assignment protocol provides a suitable basisfor subsequent NOE assignment.

Example 18 GFT NOESY-Based Protocol—NOE Peak Assignment and DistanceConstraints

A single 3D [H]-NOESY-[CH^(ali)/CH^(aro)/NH] data set recorded in 9.1hours (Table 11; corresponding to ˜1.5-2 days with a conventional probe)provided the information of all three 3D NOESY experiments routinelyacquired for structure determination of ¹³C/¹⁵N labeled proteins. Atotal of 4708 NOEs were assigned and yielded 1453 ¹H—¹H upper distancelimit constraints (Table 12). Out of the 280 long-range constraints,only 53 (19%) involved aromatic protons. However, calculations with theprogram QUEEN (Nabuurs et al., J. Am. Chem. Soc. 125:12026-12034 (2003),which is hereby incorporated by reference in its entirety) confirmed(Wüthrich, NMR of Proteins and Nucleic Acids Wiley: New York (1986);Skalicky et al., J. Am. Chem. Soc. 123:388-397 (2001), which are herebyincorporated by reference in their entirety) that these aromaticconstraints were highly valuable for the three-dimensional structuredetermination; 8 (27%) out of the 30 most informative constraints withthe largest I_(ave)/I_(total) [and 6 (40%) out of 15 most informative]involved aromatic rings (see also FIG. 38). This finding emphasized theimportance of including aromatic protons into the simultaneous NOESYdata acquisition (FIG. 36(b)) to enable high-quality NMR structuredetermination. TABLE 12 Statistics of YqfB(1-103) StructureCalculations^(a) 1. without SSA 2. PDB 3. refined Stereospecificassignments (SSA)^(b) [%] ^(β)CH₂ — 34 34 Val and Leu isopropyl groups —58 58 Conformationally-restricting distance constraints^(c) betweenresidues i and j intra-residue [i = j] 463 454 466 sequential [i − j =1] 496 511 527 medium range [1 < |i − j| <= 5] 177 208 211 long range[|i − j| > 5] 304 280 289 total 1440 1453 1493 Number of constraints perresidue 15.3 15.4 15.8 Number of long-range constraints per residue 2.92.7 2.8 DYANA target function [Å²] 1.73 ± 0.17 1.89 ± 0.16 1.72 ± 0.20Average pairwise r.m.s.d. [Å] to the mean coordinates for residues 4-101Backbone N, C^(α), C′ 0.97 ± 0.22 0.65 ± 0.18 0.69 ± 0.16 All heavyatoms 1.58 ± 0.24 1.19 ± 0.25 1.25 ± 0.21 Backbone + best definedside-chains^(d) 1.05 ± 0.15 1.00 ± 0.11 0.79 ± 0.09 Average number ofdistance constraint violations per DYANA conformer 0.2-0.5 Å 1.0 1.11.0 >0.5 Å 0 0 0 Average number of dihedral-angle constraint 0 0 0violations per DYANA conformer >5° Ramachandran map statistics Residuesin most favored regions (%) 71 73 73 Residues in additional allowedregions (%) 23 25 25 Residues in generously allowed regions (%) 5 2 2Residues in disallowed regions (%) 1 0 0^(a)20 conformers with lowest DYANA target function values out of 100calculated for YqfB (excluding the N-terminal 22-residue tag). 1. “PDB”is the reference structure deposited (1TE7) in the PDB (Berman et al.,Nucleic Acids Res. 28: 235-242 (2000), which is hereby incorporated byreference in# its entirety). 2. “without SSA” is the reference structure calculatedwith the constraint input of the PDB structure omitting thestereospecific assignments (SSA). 3. “refined” is PDB structure refinedwith NOEs resolved in the shift doublet spectra of (4,3)D[HC^(ali)/HN]-NOESY-[CH^(ali)/NH].^(b)Relative to pairs with non-degenerate chemical shifts.^(c)Note that the numbers vary for “without SSA” and “PDB” due tohandling of stereospecific assignments (Guntert et al., J. Mol. Biol.273: 283-298 (1997), which is hereby incorporated by reference in itsentirety).^(d)Best-defined side-chains include residues 7, 16, 22-25, 35, 37-39,52, 55-67, 71, 77, 79, 81, 84-86, 93, 97, 98.

Example 19 GFT NOESY-Based Protocol—YqfB Reference StructureDetermination

A high-quality NMR structure of YqFB (PDB ID: 1TE7) was obtained withthe distance constraints derived from 3D[H]-NOESY-[CH^(ali)/CH^(aro)/NH], as is evidenced (see middle columnlabeled PDB in Table 12) by (i) the small size and number of residualconstraint violations, (ii) average r.m.s.d. values relative to the meancoordinates of 20 conformers of 0.65±0.18 Å for the backbone and1.19±0.25 Å for all heavy atoms, (iii) a large fraction ofstereospecific assignments for β-methylene and the Val and Leu isopropylmoieties, and (iv) the fact that all φ and Ψ dihedral angles werelocated in the allowed (most favored, additionally or generouslyallowed) regions of the Ramachandran map.

Example 20 GFT NOESY-Based Protocol—Sensitivity of NOE Detection in(4,3)D [HC ^(ali)/HN]-NOESY-[CH^(ali)/NH]

Sensitivity of NOE detection was critical for identifying the optimaluse of (4,3)D [HC ^(ali)/HN]-NOESY-[CH^(ali)/NH]. First, the relativeintrinsic sensitivity of 3D [H]-NOESY-[CH^(ali)/CH^(aro)/NH] andseparately acquired 3D ¹⁵N-, ¹³C^(aliphatic)- and¹³C^(aromatic)-resolved [¹H,¹H]-NOESY was evaluated. Complementingprevious assessments (Farmer et al., J. Biomol. NMR 4:673-687 (1994);Pascal et al., J. Magn. Reson. 103:197-201 (1994); Jerala et al., J.Magn. Reson. B108:294-298 (1995); Uhrin et al., J. Biomol. NMR18:253-259 (2000); Xia et al., J. Biomol. NMR 27:193-203 (2003), whichare hereby incorporated by reference in their entirety), differences insensitivity arose because (i) a ¹⁵N,¹H-sensitivity enhancement scheme(Cavanagh et al., Protein NMR Spectroscopy Academic Press: San Diego(1996), which is hereby incorporated by reference in its entirety) hadnot been integrated in simultaneous [¹⁵N,¹H]/[¹³C,¹H]-HSQC detectionmodules, which reduced the sensitivity of the ¹⁵N-resolved part to ˜70%(˜1/√2) compared to a sensitivity enhanced ¹⁵N-resolved [¹H,¹H]-NOESY,(ii) a compromise value was chosen for the ¹³C—¹H INEPT delay (FIG. 36)in order to enable simultaneous detection of NOEs on aliphatic andaromatic protons, which attenuated ¹³C—¹H detected signals by ˜5%, and(iii) off-resonance effects of 90° r.f. pulses on ¹³C^(aromatic) leadingto a sensitivity reduction to ˜75%. Additional smaller losses arosebecause (i) the ¹H—¹⁵N INEPT (Cavanagh et al., Protein NMR SpectroscopyAcademic Press: San Diego (1996), which is hereby incorporated byreference in its entirety) delay (5.4 ms) was longer than the ¹³C—¹HINEPT delay (3.4 ms), which increased the signal loss for the¹³C-resolved part due to T₂(¹H) relaxation during an additional periodof 4 ms, and (ii) of longer maximal evolution times in t₂ for ¹⁵Nfrequency (˜16 ms) than for ¹³C^(aliphatic)/¹³C^(aromatic) frequencylabeling (˜6 ms), which requires that longitudinal two-spin order,H_(z)C_(z), is present prior and after frequency ¹³C labeling leading tosome signal loss for ¹³C—¹H detected signals due to T₁(H_(z)C_(z))relaxation. Taken together, sensitivity is reduced relative to separatedata acquisition to ˜70% for the ¹⁵N-resolved, to ˜80% for the¹³C^(aliphatic)-resolved, and to ˜65% for the ¹³C^(aromatic)-resolvedpart. Requiring that the same S/N ratios are obtained in simultaneous 3DNOESY as in the separately acquired spectra, one obtains an effectiveacceleration of data acquisition speed by ˜1.5. (Following thesesensitivity considerations, the impact of simultaneous NOESY acquisitionon NMR data collection speed shall be illustrated. For example, one canassume that ¹⁵N-resolved, ¹³C^(aliphatic)-resolved and¹³C^(aromatic)-resolved NOESY are acquired in 12 hours each (yielding 36hours total measurement time). About 30-35% sensitivity is lost due tosimultaneous acquisition for ¹⁵N-resolved as well as for the¹³C^(aromatic) resolved part. To compensate for these losses, themeasurement time needs to be doubled. As a result, data collection speedis effectively increased by a factor of 1.5 (24 hours instead of 36hours). Notably, use of a simultaneous [¹⁵N,¹H]/[¹³C,¹H]-HSQC detectionmodule (Sattler et al., J. Biomol. NMR 5:97-102 (1995), which is herebyincorporated by reference in its entirety) could increase thesensitivity of the ¹⁵N-resolved part.)

Next, the sensitivity of central peak detection in 3D[H]-NOESY-[CH^(ali)/CH^(aro)/NH] was compared with shift doubletdetection in (4,3)D [HC ^(ali)/HN]-NOESY-[CH^(ali)/NH]. Since the shiftdoublets arose from an in-phase splitting of the central peaks, theintrinsic sensitivity of detecting each peak of a shift doublet was apriori reduced to 50% when compared with central peak detection.However, the fact that only shift doublets represent viable signalsallowed one to identify peaks significantly closer to the noise level(Szyperski et al., J. Am. Chem. Soc. 115:9307-9308 (1993), which ishereby incorporated by reference in its entirety). This compensated, atleast partly, for the 2-fold loss in sensitivity. The sensitivity ofshift doublet detection was further reduced due to the transverserelaxation occurring during the additional simultaneous[¹⁵N,¹H]/[¹³C,¹H]-HSQC module (FIG. 36). This loss depends on proteinsize and shape, which determine the correlation time(s) for the overallrotational tumbling, as well as internal mobility. For a rigid sphericalprotein, calculation of ¹H^(N), ¹⁵N, ¹H^(aliphatic), and ¹³C^(aliphatic)(non-methyl) transverse relaxation rates (Cavanagh et al., Protein NMRSpectroscopy Academic Press: San Diego (1996), which is herebyincorporated by reference in its entirety) is feasible. This allows oneto estimate, with the transfer delays defined in FIG. 36(a), thereduction of sensitivity as a function of the correlation time forisotropic reorientation (FIG. 39). For YqfB (τ_(r)˜7.7 ns), theory(Cavanagh et al., Protein NMR Spectroscopy Academic Press: San Diego(1996), which is hereby incorporated by reference in its entirety)predicted (FIG. 39) that relaxation would further reduce S/N ratios ofshift doublet components to, respectively, ˜38% and ˜28% of thesensitivity of central peak detection after a splitting with Ω(¹⁵N) andΩ(¹³C) is encoded. Additional smaller losses can be expected to arisefrom (i) signal de-phasing due to the presence of passive one-bond¹³C—¹³C, and one- and two-bond ¹⁵N—¹³C^(α) scalar couplings, (ii) r.f.pulse inhomogenities, and (iii) r.f. pulse off-resonance effects. (Notethat for ¹³C^(aliphatic)-resolved shift doublets, a slight gain insensitivity relative to central peak detection in 3D[H]-NOESY-[CH^(ali)/CH^(aro)/NH] was due to the fact the ¹³C—¹H INEPTdelay was not tuned to a compromise value; FIG. 36.) Experimentally, itwas observed that the S/N of the peaks constituting the shift doubletswas reduced to ˜30±5% for ¹⁵N-resolved, and to ˜29±6% (non-methyl) and˜37±4% (methyl) for ¹³C-resolved central peaks. These values were ingood agreement with the theoretical estimates (FIG. 39), suggesting thatthese allow one to assess the role of (4,3)D [HC^(ali)/HN]-NOESY-[CH^(ali)/NH] for larger systems.

Example 21 GFT NOESY-Based Protocol—Completeness of Central Peak VersusShift Doublet Detection

The 3D [H]-NOESY-[CH^(ali)/CH^(aro)/NH] was acquired in 9.1 hours (Table11). Considering that the sensitivity for detecting each peak of a shiftdoublet was only ˜30% of the sensitivity for central peak detection (seeExample 20; FIG. 39), ten-fold longer measurement time, i.e., about 90hours, would be required to achieve comparable completeness of NOEdetection in central peak and shift doublet subspectra. This appeared tobe inappropriately long considering that through-bond GFT NMR and 3DNOESY spectra required for structure determination of YqfB were recordedin 26 hours (Table 11). Importantly, it may well suffice to detect shiftdoublets only for stronger NOEs in order to increase the fraction ofassigned long-range NOEs to a level that an accurate initial structurecan be calculated. Hence, for shift doublet data sets recorded with 30hours (data set I) and 60 hours (data set II) of measurement time, thefraction of NOEs in 3D [H]-NOESY-[CH^(ali)/CH^(aro)/NH] was determinedfor which a corresponding shift doublet peak was detected. In data set I(data set II), 75% (93%) of the ¹⁵N-resolved long-range NOEs (total:104) and 64% (95%) of the ¹³C^(aliphatic)-resolved long-range NOEs(total: 225) were detected. (Similar fractions were obtained formedium-range NOEs assigned based on chemical shifts in 3D NOESY/3D NOESYplus shift doublet data set I/3D NOESY plus shift doublet data set II:¹⁵N-resolved NOEs (total: 114) 21%/53%/72%; ¹³C^(aliphatic)-resolvedNOEs (total: 90) 14%/64%/76%. Moreover, 60%/100%/100% was obtained forlong-range H^(N)—H^(N) (total: 25) and 29%/69%/83% for long-rangeCH₃—CH₃ NOEs (total: 29).) Hence, the majority of long-range NOEs weredetected after 30 hours measurement time, while NOE detection approachedcompleteness (relative to 3D [H]-NOESY-[CH^(ali)/CH^(aro)/NH]) only wheninvesting 60 or more hours of spectrometer time. Thus, it was proposedthat, for proteins up to ˜15-20 kDa (τ_(r)˜8-10 ns), the measurementtime for shift doublet detection should be ˜2-3 times longer than thatfor central peak detection. Considering increased losses due to spinrelaxation at longer τ_(r) (FIG. 39), it was anticipated that 3-4 timeslonger measurement times would be required for larger proteins in the20-25 kDa range (τ_(r)˜10-13 ns).

Example 22 GFT NOESY-Based Protocol—Chemical Shift-Based Unambiguous NOEAssignment

The fraction of NOEs which can be unambiguously assigned directly fromchemical shift data represents a key “figure of merit” determining therobustness of an NMR structure determination protocol (Güntert, Prog.NMR Spectroscopy 43:105-125 (2003); Baran et al., Chem. Reviews104:3451-3455 (2004); Huang et al., Methods Enzymol. 394:111-141 (2005),which are hereby incorporated by reference in their entirety). Hence, itwas examined to which extent the measurement of the fourth chemicalshift encoded in the splitting of the shift doublets resolve assignmentambiguities encountered in 3D NOESY (FIG. 40).

Among the long-range NOEs in 3D [H]-NOESY-[CH^(ali)/CH^(aro)/NH], only33% of the ¹⁵N-resolved and 18% of the ¹³C^(aliphatic)-resolved NOEs canbe assigned without reference to an (initial) structure. Whenconsidering also the 4D information encoded in the shift doublets ofdata set I (data set II), these fractions increase to 74% (88%) and 71%(83%). Hence, most shift doublets can be unambiguously assigned based onchemical shifts; that is, the detection yield of shift doublets largelydetermines the fraction of unambiguously assigned NOEs (FIG. 40).

Example 23 GFT NOESY-Based Protocol—Additional NOEs Resolved in ShiftDoublet Subspectra

Due to the lower sensitivity of shift doublet detection, one expects toregister only those NOEs as shift doublets which are also present in 3D[H]-NOESY-[CH^(ali)/CH^(aro)/NH] as central peaks. However, peak overlapand cases of severe chemical shift degeneracy quite generally preventone from completely assigning peaks in 3D[H]-NOESY-[CH^(ali)/CH^(aro)/NH], even with reference to a high-qualitystructure (for YqfB, 86% of all NOE peaks could be assigned). Analysisof the shift doublet subspectra of data set II yielded 22 unidentified(new) ¹⁵N-resolved and 19 ¹³C^(aliphatic)-resolved NOEs. Hence, as longas the measurement time invested for shift doublet and central peakacquisition are similar, shift doublets are primarily expected to play akey role for assigning central peak NOEs in 3D NOESY. Otherwise, exceptfor small proteins, comparably few new distance constraints areanticipated.

Example 24 GFT NOESY-Based Protocol—QUEEN Analysis of NOE ConstraintNetworks

Depending on their uniqueness, upper distance limit constraints vary intheir impact on structure determination and refinement. Hence, reportingthe sheer number of NOEs (Table 12) provided only a semiquantitativeassessment of the constraint network obtained with a given protocol.Recently, the algorithm and program QUEEN (Nabuurs et al., J. Am. Chem.Soc. 125:12026-12034 (2003), which is hereby incorporated by referencein its entirety) were devised to quantify information contained inexperimental NMR data by information theoretical analysis in distancespace. QUEEN was used to evaluate the long-range constraint networksobtained for protein YqfB when recording (4,3)D [HC^(ali)/HN]-NOESY-[CH^(ali)/NH] acquired with 3D[H]-NOESY-[CH^(ali)/CH^(aro)/NH] for central peak detection (FIG. 38).As expected, the total information, I_(total), of the referenceconstraint list (1.577 bits/atom²) was significantly higher thanI_(total) of the constraint list derived from 3D NOESY with solereference to chemical shifts (1.327 bits/atom²). In contrast, I_(total)of the constraint lists derived with reference to (4,3)D [HC^(ali)/HN]-NOESY-[CH^(ali)/NH] shift doublet data sets I and II (1.539and 1.547 bits/atom²) were nearly the same and also quite similar toI_(total) of the reference list. This showed that shift doublet data setI (30 hours measurement time) enabled one to derive the major fractionof the final I_(total), predicting that an accurate initial structurecan be obtained from the thus obtained initial constraint network.

Furthermore, a calculation of the distribution of unique information,I_(uni), and average information, I_(ave), of the constraints yieldingthe reference structure (1TE7) confirmed that chemical shift based NOEassignment identified constraints irrespective of their location in the[I_(uni), I_(ave)] plot; that is, the highly informative constraintswere identified with the same probability as those with a lowinformation content (FIG. 38(a)). This feature of shift based NOEassignment was in contrast to what can be expected for the algorithmimplemented in the program CYANA. Network anchoring (Herrmann et al., J.Mol. Biol. 319:209-227 (2002), which is hereby incorporated by referencein its entirety) favors identification of distance constraints withcomparably lower information content, since the constraints with highinformation content are not embedded in a (dense) network which mightserve for assignment. As a result, constraints identified forcalculating an initial CYANA structure represented less information inthe context of the final constraint network (FIG. 38(b)). This mightimply that, in general, initial structures derived from (4,3)D NOESY maybe more accurate than those obtained with CYANA from 3D NOESY.

Example 25 GFT NOESY-Based Protocol—Comparative NMR StructureCalculations

Comparative structure calculations were performed to explore the impactof NOEs which could be assigned directly based on chemical shift datawhen having shift doublet data sets I or II along with 3D[H]-NOESY-[CH^(ali)/CH^(aro)/NH] (Table 13; FIGS. 41 and 42). As usual,mean pairwise r.m.s.d. values were calculated relative to meancoordinates in order to assess the precision of the resulting bundles ofconformers. Stereospecific assignments, which are mostly obtained duringthe last stages of structural refinement by using the GLOMSA module ofDYANA (Güntert et al., J. Mol. Biol. 273:283-298 (1997), which is herebyincorporated by reference in its entirety), were not considered. Hence,precision was assessed relative to a YqfB structure obtained with theNOEs used for the PDB structure (1TE7) but after omission of allstereospecific assignments (column 1 in Table 12 denoted “without SSA”).Accuracy was assessed by calculating the r.m.s.d. values between themean coordinates of the resulting bundle of conformers and the meancoordinates of the reference structure of YqfB deposited in the PDB ID1TE7 (column 2 in Table 12 denoted “PDB”). Assuming a small number of(unavoidable) human errors for NOE assignment (see Example 15), it iscertainly so that the “true” structure is somewhere “in between” themanual structure and the structures obtained either with reduced NOEconstraint input or with automated methods. However, NOE assignmentswere carefully double-checked by visual line-shape comparison, whichensured that the remaining number of assignment errors was very small.Clearly, automated methodology relying on chemical shift data onlycannot accomplish the same high reliability. Hence, for the experimentdisclosed herein, it was assumed that the manual structure represented,in a good approximation, a “gold standard” for benchmarking thealternative structure determination protocols. A summary of r.m.s.d.values obtained from the comparative structure calculations is given inTable 13 and FIG. 41. TABLE 13 R.m.s.d. Values of Comparative NMRStructure Calculations r.m.s.d^(a) [Å] Precision^(c) Accuracy^(d)Structure^(b) Backbone Heavy atoms Backbone Heavy atoms (1.) Reference(PDB ID 1TE7) (×)^(e) 0.65 ± 0.18 1.19 ± 0.25 — — (2.) Reference (“noSSA”) (+)^(f) 0.97 ± 0.22 1.58 ± 0.24 1.28 1.62 (3.) 3D NOESY and shiftsonly (▪)^(g) 4.02 ± 1.03 5.00 ± 0.96 3.22 3.70 (4.) 3D NOESY andshifts + (4,3) 1.97 ± 0.44 2.86 ± 0.46 1.58 2.27    D dataset “I”(●)^(h) (5.) 3D NOESY and shifts + (4,3) 1.53 ± 0.28 2.42 ± 0.33 1.351.80    D dataset “II” (◯)^(h) (6.) CYANA (1^(st) Cycle) (▾)^(i) 2.18 ±0.49 2.96 ± 0.55 2.81 3.69 (7.) CYANA starting from (4.) (▴)^(j) 0.82 ±0.19 1.35 ± 0.23 1.57 2.17 (8.) CYANA staring from (5.) (Δ)^(j) 0.90 ±0.18 1.46 ± 0.22 1.58 2.17^(a)R.m.s.d. values were calculated for residues 4-101 of YqfB. For agraphical representation of the values, see FIG. 41.^(b)Symbols provided in parentheses are those identifying thecorresponding bundle in FIG. 42.^(c)Precision was assessed by calculating the mean pairwise r.m.s.d. forthe bundle of NMR conformers relative to their mean coordinates.^(d)Accuracy was assessed by calculating the r.m.s.d. between the meancoordinates of the bundle of NMR conformers and the reference structure.^(e)Reference structure.^(f)Reference structure calculated after omission of stereospecificassignments (see Table 12).^(g)Initial structure calculated from NOEs assigned in 3D[H]-NOESY-[CH^(ali)/CH^(aro)/NH] based on chemical shift data only.^(h)Initial structure calculated from NOEs assigned in 3D[H]-NOESY-[CH^(ali)/CH^(aro)/NH] based on chemical shift data only butwith reference to shift doublet datasets I and II of (4,3)D[HC^(ali)/HN]-NOESY-[CH^(ali)/NH].^(i)Initial structure calculated with the program CYANA in the 1^(st)cycle using the final 3D [H]-NOESY-[CH^(ali)/CH^(aro)/NH] peak list usedfor determining the reference structure (PDB ID 1TE7).^(j)Structures calculated with the program CYANA when starting with theconstraint input yielding the structures indicated with footnote “h”.A. Impact on Precision of Initial Structure

For comparison of precision, r.m.s.d. values were calculated for astructure obtained with the NOE input used for determining the referenceYqfB structure (1TE7; FIG. 42(a)), except that stereospecificassignments were omitted. This yielded r.m.s.d. values of 0.97±0.22 Å(FIG. 42(b)) and 1.58±0.24 Å for backbone and heavy atoms of residues4-101, respectively (Tables 12 and 13). As expected, a structure ofrather low precision was obtained when considering solely long-rangeNOEs which can be assigned in 3D [H]-NOESY-[CH^(ali)/CH^(aro)/NH] basedon shift data; the corresponding r.m.s.d. values were 4.02±1.03 Å (FIG.42(c)) and 5.00±0.96 Å, respectively. Evidently, if the structurerefinement is to be completed using manual methods with the 3D NOESYdata set alone, great care would be necessary to ensure properconvergence. When including also NOEs that could be assigned withreference to the shift doublets detected in data set I (or data set II),these values dropped to 1.97±0.44 Å (FIG. 42(d)) (1.53±0.28 Å; FIG.42(e)) and 2.86±0.46 Å (2.42±0.33 Å). This showed that (i) the 4Dinformation encoded in (4,3)D [HC ^(ali)/HN]-NOESY-[CH^(ali)/NH] allowedone to generate quite precise initial structures, and (ii) the structureobtained with data set I exhibited r.m.s.d. values which were only ˜1 Åabove those of the reference structure (calculated after omission ofstereospecific assignments; Table 12). The r.m.s.d values wereconsistent with the finding that ˜70-75% (˜80-90%) of all backbone andaliphatic long-range NOEs can be assigned as central peaks in 3D NOESY(see above) when having the information of shift doublet data set I(data set II). Furthermore, the major part of the precision gap to thereference structure was due to the fact that the shift doublet spectradid not exhibit aromatic NOEs: when including all aromatic constraints,the backbone r.m.s.d. value dropped to 1.41±0.23 Å (1.12±0.17 Å for dataset II). This was close to the reference value of 0.97±0.22 Å. It wasthus concluded that, in agreement with information-theoretical QUEENanalysis of the constraint networks (FIG. 38), the measurement timeinvested for recording shift doublet data set I (30 hours) representedthe most effective approach for obtaining a precise initial fold whichensures smooth convergence of the structure refinement.

B. Impact on Accuracy of Initial Structure

The 20 best conformers representing the PDB reference structure wereused to assess accuracy and exhibited mean r.m.s.d. values of 0.65±0.18Å (backbone) and 1.19±0.25 Å (all heavy atoms) relative to the meancoordinates of residues 4-101 (Table 12). These r.m.s.d. values define,arguably somewhat arbitrarily, the “allowed conformational space”associated with the reference structure. An initial structure wasconsidered as “accurate” if the conformational space associated with theinitial structure overlapped with the allowed conformational space. Thiscriterion was fulfilled if the r.m.s.d values calculated between themean coordinates of initial and reference structure was smaller than thesum of the mean r.m.s.d. values to the mean coordinates of the twostructure calculations. Root mean square deviation calculations showedthat initial structures derived from NOEs assigned based on chemicalshift data were accurate (Table 13; FIGS. 41 and 42). In fact, theinitial structures were accurate enough to even have the meancoordinates of the reference structure located within their allowedconformational space.

C. Comparison with CYANA's Initial Structure

To compare the impact of (4,3)D [HC ^(ali)/HN]-NOESY-[CH^(ali)/NH] dataacquisition versus an approach to automatically assign NOEs in 3D NOESY,a CYANA (Herrmann et al., J. Mol. Biol. 319:209-227 (2002), which ishereby incorporated by reference in its entirety) calculation wasperformed. The first cycle of a CYANA calculation generated an initialstructure by using network anchoring and constraint combination, thatis, likewise without reference to three-dimensional structural knowledge(Herrmann et al., J. Mol. Biol. 319:209-227 (2002), which is herebyincorporated by reference in its entirety). When providing only TALOSdihedral angle constraints, and intraresidue, sequential, andmedium-range ¹H—¹H upper distance limit constraints as input, along withthe unassigned reference 3D NOESY peak list, the resulting initial CYANAstructure exhibited r.m.s.d. values of 2.18±0.49 Å (backbone) and2.96±0.55 Å (all heavy atoms) relative to the mean coordinates (Table13; FIGS. 41 and 42). Hence, with the final peak list as input, thealgorithm implemented in CYANA for solving the NOE assignment problemresulted in a precision which was comparable to what was obtained with4D NOESY information (Table 13). However, the corresponding accuracyafter the 1^(st) cycle turned out to be lower than the initial structureobtained with 4D NOESY information based on chemical shifts only (Table13). This may have well been due to the fact that employment of networkanchoring could not support the assignment of NOEs with the highestinformation content (FIG. 38). This is because the high informationcontent arose from not being embedded in a (dense) NOE network (whichmay serve to “anchor” them). Moreover, it might be that use of a largernumber of ambiguous long range constraints simply led to anoverestimation of the precision of the initial structure.

D. CYANA Structures Derived from (4,3)D NOESY-Derived Initial Structures

The high accuracy of the initial folds obtained from (4,3)D [HC^(ali)/HN]-NOESY-[CH^(ali)/NH] (Table 13; FIG. 41) allows one toreliably obtain most of the remaining NOE assignments using the programCYANA. Both precision and accuracy of the obtained structures were closeto the values of the manually obtained reference structure (a slightlylower accuracy compared to the manually refined structure indicated,however, that manual intervention such as visual line shape comparison,would be required for finishing the refinement). It was thus concludedthat the combination of (4,3)D [HC ^(ali)/HN]-NOESY-[CH^(ali)/NH] withautomated structure determination protocols (Moseley et al., MethodsEnzymol. 339:91-108 (2001); Huang et al., J. Mol. Biol. 327:521-536(2003); Huang et al., J. Am. Chem. Soc. 127:1665-1674 (2005); Güntert etal., J. Mol. Biol. 273:283-298 (1997); Herrmann et al., J. Mol. Biol.319:209-227 (2002); Güntert, Methods Mol. Biol. 278:347-372 (2004),which are hereby incorporated by reference in their entirety), possiblya parallel consensus operation of bottom-up and top-down protocols,represented a powerful approach to ensure fast and robust highthroughput determination of high-quality NMR structures.

E. Refinement of YqfB Reference Structure

The reference structure (1TE7) determined with distance constraintsderived from 3D [H]-NOESY-[CH^(ali)/CH^(aro)/NH] was further refined byincorporating NOEs that could be resolved in the shift doubletsubspectra (data set II; FIG. 40). As expected, the comparably few newNOEs resulted in only a moderate increase in precision: only ther.m.s.d. value calculated for backbone and best-defined side chains(that is, the molecular core) was somewhat decreased (column 3 in Table12 denoted “refined”). This finding supported the view that shiftdoublet detection in (4,3)D [HC ^(ali)/HN]-NOESY-[CH^(ali)/NH] wasprimarily a valuable tool to assign the majority of the (stronger) NOEsdirectly based on chemical shift data only.

Example 26 GFT NOESY-Based Protocol for High-Quality Protein StructureDetermination

GFT NMR enables one to “cut the Gordian knot” and combine rapid NMR datacollection with robust, high-quality NMR structure determination. Thisis pivotal for NMR-based structural biology and genomics. The resonanceassignment is facilitated by the fact that only five GFT NMR experimentsare required, each providing 4D and 5D NMR spectral information at highdigital resolution. (4,3)D [HC ^(ali)/HN]-NOESY-[CH^(ali)/NH] acquiredwith 3D [H]-NOESY-[CH^(ali)/CH^(aro)/NH] for central peak detectionaffords the information of several 3D and 4D heteronuclear resolvedNOESY spectra and enables detection of a dense networks of ¹H—¹H upperdistance constraints, as required for high-quality structures. Themajority of NOEs detected as shift doublets can be assigned based onchemical shift data only, and assignment of the weaker NOEs, which areoften not detectable as shift doublets, is greatly facilitated by havingin a single 3D [H]-NOESY-[CH^(ali)/CH^(aro)/NH] spectrum with each X1-H¹. . . H¹—X2 NOE resolved at the chemical shift of X1 and thecorresponding to the transposed peak resolved at the chemical shift ofX2. Moreover, the impact of distance constraints referred to aromaticrings for structural refinement has long been documented (Wüthrich, NMRof proteins and Nucleic Acids Wiley: New York (1986); Skalicky et al.,J. Am. Chem. Soc. 123:388-397 (2001), which are hereby incorporated byreference in their entirety), which emphasizes the importance ofincluding ¹³C^(aromatic)-resolved [¹H,¹H]-NOESY in the scheme forsimultaneous acquisition. For proteins comprising a large number ofaromatic rings, recording of (4,3)D [HC ^(ali)/HN]-NOESY-[CH^(aro)]might be advisable. ((4,3)D [HC ^(ali),HN]-NOESY-[CH^(aromatic)] can bereadily implemented by eliminating the second [¹⁵N,¹H^(N)]-HSQC moduleand tuning the second [¹³C,¹H]-HSQC module in FIG. 36(a) for aromatic CHmoieties. Except for ¹H^(aromatic)—¹H^(aromatic) NOEs, all NOEsinvolving aromatic protons are detected in such an experiment, and allowtheir assignment based on detection of shift doublets. Considering thatthe spectral width of ¹³C^(aromatic) is about one-half of the spectralwidth of ¹³C^(aliphatic), the minimal measurement time is ˜6.5 hrs at600 MHz (i.e., about half of the minimal measurement time of thealiphatic congener; Table 11).) The present invention demonstrates that,for proteins up to ˜15-20 (˜20-25) kDa, it is recommended to acquire theshift doublet subspectra with ˜2-3 (˜3-4) times of the measurementrequired for 3D [H]-NOESY-[CH^(ali)/CH^(aro)/NH] (the central peakspectra). This suffices to assign most of the stronger NOEs by detectionof shift doublets, and the thus obtainable precise and accurate initialstructures ensure rapid convergence of the structure refinement. Forsmaller proteins, it can be envisaged that (4,2)D [HC^(ali)/HN]-NOESY-[CH^(ali)/NH] or (3,2)D[H]-NOESY-[CH^(ali)/CH^(aro)/NH] are valuable tools to study proteinstructure and folding. In (4,2)D ¹⁵N/¹³C^(aliphatic) [¹H—¹H] NOESY,magnetization is first transferred from given ¹H nucleus to its directlyattached heteroatom (¹⁵N/¹³C^(aliph)) which is frequency labeled inconjunction with ¹H during τ₁(ω₁). Subsequently, magnetization istransferred through the nuclear Overhauser effect to all ¹H spins thatare located within ˜5 Å in space. The resulting ¹H magnetization istransferred again to its directly attached heteroatom for frequencylabeling (¹⁵N/¹³C^(aliph)) along ω₁, before transferring back for directdetection. The peak patterns observed in this experiment is shown inFIG. 43 and the r.f pulse scheme is shown in FIG. 44. In (3,2)D¹⁵N/¹³C^(aliphatic)-resolved [¹H—¹H] NOESY, after frequency labeling ofa given ¹H nucleus along ω₂, magnetization is transferred through thenuclear Overhauser effect to all ¹H spins that are located within ˜5 Åin space. Subsequently, magnetization from ¹H is transferred to itsdirectly attached heteroatom (¹⁵N/¹³C^(aliph)) for frequency labelingalong ω₁ and back for direct detection (ω₁). The peak pattern observedin this experiment is shown in FIG. 45 and the r.f pulse scheme is shownin FIG. 46. Table 14 shows the acquisition parameters for the (4,2)D [HC^(ali)/HN]-NOESY-[CH^(ali)/NH] and (3,2)D[H]-NOESY-[CH^(ali)/CH^(aro)/NH] experiments. TABLE 14 AcquisitionParameters for GFT NMR Experiments Recorded for 15 kDa Protein ET99(3,2)D (4,2)D ¹⁵N/¹³C^(aliphatic)[¹H,¹H]- ¹⁵N/¹³C^(aliphatic)[¹H,¹H]-NOESY NOESY ¹H resonance frequency 750 MHz 750 MHz No. of Points (t₁,t₂) 256, 512 320, 512 Collected: After LP: 256, 512 320, 512 After zerofilling: 512, 64, 1024 512, 64, 1024 Window functions: sine 70/70 sine70/70 No. of transients: 4   4   Spectral width 16000, 8000 20000, 8000(ω₁, ω₂; Hz) t_(max) (ms) 16.0, 64.0 16.0, 64.0 Carrier Position4.78/36/118.0, 4.78 4.78/36/119, 4.78 (ω₁, ω₂; ppm) Recycle delay(s) 1.01.0 Collection time (hrs) 0.3 0.4

In the future, new software for efficiently symmetrizing (Szyperski etal., J. Magn. Reson. B108:197-203 (1995), which is hereby incorporatedby reference in its entirety) (4,3)D [HC ^(ali)/HN]-NOESY-[CH^(ali)/NH]subspectra about the position of the central peaks along the GFTdimension will allow one to increase the effective S/N ratio of theshift doublets. (With such software, the precision and accuracy of theinitial structure obtained with data set II (60 hours measurement time;Table 13; FIGS. 41 and 42) can be expected to be obtained with data setI (30 hours measurement time).) This will further reduce the NMRmeasurement time required for (4,3)D NOESY and/or increase itsfeasibility for large proteins, and combination of (4,3)D [HC^(ali)/HN]-NOESY-[CH^(ali)/NH] with automated structure determinationprotocols promises to be an ideal choice for high throughputdetermination of proteins.

Example 27 Implementation of J-GFT (6,2)D (H^(α)—C^(α)—CO)—N—HN

The r.f. pulse scheme of J-GFT (6,2)D (H^(α)—C^(α)—CO)—N—HN (FIG. 47)was derived from previously published (5,2)D HACACONHN (Kim et al., J.Am. Chem. Soc. 125:1385-1393 (2003); Kim et al., J. Biomol. NMR28:117-130 (2004), which are hereby incorporated by reference in theirentirety). Except for Ω(¹⁵N), chemical shifts were refocused duringconstant-time delays serving for polarization transfer and evolution ofcouplings. In contrast to IPAP (Ottiger et al., J. Magn. Reson.131:373-378 (1998), which is hereby incorporated by reference in itsentirety) and other spin-state filtered experiments (Meissner et al., J.Magn. Reson. 128:92-97 (1997); Sørensen et al., J. Biomol. NMR10:181-186 (1997); Andersson et al., J. Biomol. NMR 12:435-441 (1998),which are hereby incorporated by reference in their entirety), noadditional delays were required to generate transfer amplitudes whichwere either cosine or sine modulated by the coupling evolutions.

The acquisition scheme of FIG. 47 can be readily understood whenconsidering the r.f. pulse module depicted in FIG. 48 since this modulewas repeatedly incorporated for simultaneous measurement of multipleRDCs during polarization transfers. Cosine or sine-modulations wereachieved during I-S polarization transfers while I-S anti-phasemagnetization was refocused to in-phase transverse S magnetization (FIG.48), which then led to observable magnetization during signal detection.With I and S representing the product operators (Sørensen et al., Prog.NMR Spectrosc. 16:163-192 (1983), which is hereby incorporated byreference in its entirety) of spins I and S, and ¹J, ¹D and ¹Kindicating scalar coupling, RDC and their sum, respectively, one obtainsat τ=½J_(IS) for the “cosine modulated data set”I _(z) S _(y) (at point a)→S _(x) sin[π¹ K _(IS)(τ+t ₁)]=S _(x) cos[π¹ K_(IS) t ₁+φ] with φ=π/2(¹ D/ ¹ J) (at point b in FIG. 48)  (20),and for the “sine modulated data set”I_(z)S_(y) (at point a)→S_(x) sin(π¹K_(IS)t₁) (at point b in FIG.48)  (21).

Although being a scalar quantity, the coupling K_(IS) is thus measuredin a “pseudo phase-sensitive manner”, that is, two subspectra areacquired in which the transfer amplitude is either cosine or sinemodulated. As a result, the coupling evolution can formally be treatedlike a chemical shift and several couplings can be jointly sampled aswas introduced for chemical shifts in the framework of GFT NMRspectroscopy (Kim et al., J. Am. Chem. Soc. 125:1385-1393 (2003), whichis hereby incorporated by reference in its entirety). Then, a G-matrixtransformation of the time domain data yields subspectra in which linearcombinations of couplings (and chemical shifts) are measured and thedifferent linear combinations are edited into different subspectra.

For (6,2)D (H^(α)—C^(α)—CO)—N—HN (FIG. 47), the backbone ¹⁵N shift wasdetected in quadrature and the multiplets of the basic spectra (Kim etal., J. Am. Chem. Soc. 125:1385-1393 (2003), which is herebyincorporated by reference in its entirety) encoded along with Ω(¹⁵N) thefour mutually correlated one-bond couplings ¹K_(C)α_(H)α, ¹K_(C)α_(C′),¹K_(NC′) and ¹K_(NH) (FIG. 49). Unambiguous grouping of multipletcomponents in cases of ¹⁵N,¹H^(N)-shift degeneracy can be accomplishedby central peak detection, as introduced in reduced-dimensionality (RD)NMR spectroscopy (Szyperski et al., J. Am. Chem. Soc. 115:9307-9308(1993); Szyperski et al., J. Magn. Reson. Ser. B 108:197-203 (1995);Szyperski et al., J. Am. Chem. Soc. 118:8146-8147 (1996); Szyperski etal., Proc. Natl. Acad. Sci. USA 99:8009-8014 (2002); Brutscher et al.,J. Magn. Reson. Ser. B 105:77-82 (1994); Szyperski et al., J. Magn.Reson. Ser. B 105:188-191 (1994); Szyperski et al., J. Biomol. NMR11:387-405 (1998), which are hereby incorporated by reference in theirentirety). The choice of a particular scheme for central peak detectionis guided by experimental sensitivity and one may also consider that theprecision of the measurements depends on the degree ofover-determination (Kim et al., J. Am. Chem. Soc. 125:1385-1393 (2003),which is hereby incorporated by reference in its entirety). For theimplementation of (6,2)D (H^(α)—C^(α)—CO)—N—HN, the following wasencoded: (i) ¹³C^(α)—¹³C′, ¹⁵N—¹³C′, ¹⁵N—H^(N) couplings and ¹⁵N shiftsin 1^(st) order central peak spectra, (ii) ¹⁵N—¹³C′, ¹⁵N—¹H^(N)couplings and ¹⁵N shifts in 2^(nd) order central peak spectra, (iii)¹⁵N—¹H^(N) couplings and ¹⁵N shifts in 3^(rd) order central peakspectra, and (iv) ¹⁵N shifts in 4^(th) order central peak spectra.Hence, a total of 31 2D planes constituted the (6,2)D(H^(α)—C^(α)—CO)—N—HN experiment (resulting in a minimal requiredmeasurement time of 31 times 1.5 min=47 min), and ¹⁵N—¹H^(N) (˜92 Hz),¹⁵N—¹³C′ (˜15 Hz), ¹³C^(α)—¹³C (˜55 Hz), and ¹³C^(α)—¹H^(α) (˜135 Hz)couplings were obtained from a least squares fit to linear combinationsof couplings detected in, respectively, 30, 28, 24, and 16 subspectra.Such a peak pattern is illustrated in FIG. 50(a). This experiment canalso be used to measure the residual dipolar complings (RDC) forproteins dissolved in liquid crystalline media as shown in FIG. 50(b).Table 15 shows the acquisition parameters for the (6,2)D(H^(α)—C^(α)—CO)—N—HN experiment. TABLE 15 Acquisition Parameters forGFT NMR Experiments Recorded for 8.0 kDa Protein Z-domain RDCs RDCs(isotropic state) (partially aligned state) ¹H resonance frequency 750MHz 750 MHz No. of Points (t₁, t₂) Collected: 50, 512 50, 512 After LP:50, 512 50, 512 After zero filling: 512, 1024 512, 1024 Windowfunctions: sine 70/70/70 sine 70/70/70 No. of transients: 64 128Spectral width (ω₁, ω₂, ω₃; Hz) 2000, 8000  2000, 8000  t_(max) (ms)24.5, 64.0  24.5, 64.0  Carrier Position (ω₁, ω₂; ppm) 118.9, 4.78 118.9, 4.78  Recycle delay(s) 1.0 1.0 Collection time (hrs) 24.0 48.0

Importantly, the constant-time evolution (Cavanagh et al., Protein NMRSpectroscopy Academic Press: San Diego, Calif. (1996), which is herebyincorporated by reference in its entirety) of couplings (FIG. 47)prevents line broadening when measuring multiple RDCs simultaneously, aswas discussed for simultaneous measurement of several chemical shifts(Kim et al., J. Am. Chem. Soc. 125:1385-1393 (2003), which is herebyincorporated by reference in its entirety). Furthermore, cancellationartifacts due to differential relaxation are avoided. To minimize linebroadening due to passive ¹H—¹H RDCs, ¹K_(C)α_(H)α-evolution ispreferably accomplished while transverse ¹³C^(α) magnetization ispresent for ¹³C^(α)—¹³C′ INEPT, and not at the start of the experimentwhen transverse ¹H^(α) magnetization is present. Since the correspondingINEPT delay is set to 8.8 ms, ¹K_(C)α_(H)α-evolution has to be scaleddown by a factor ⅓ in order to achieve a maximal evolution time of ˜25ms for Ω(¹⁵N) and the other couplings (notably, ¹K_(C)α_(C′)-evolutionis accomplished during the long ¹³C′—¹⁵N transfer step of ˜30 ms).

Example 28 J-GFT (6,2)D (H^(α)—C^(α)—CO)—N—HN NMR Data Acquisition andProcessing

RDCs were extracted from (6,2)D (H^(α)—C^(α)—CO)—N—HN experimentsacquired at 25° C. for (i) a ˜1 mM ¹³C/¹⁵N doubly labeled solution ofthe protein Z-domain (Zheng et al., Protein Sci. 13:549-554 (2004),which is hereby incorporated by reference in its entirety) (M_(r)˜8kDa), and (ii) a ˜0.5 mM solution aligned with Pf1 phages (Hansen etal., Nat. Struct. Biol. 5:1065-1074 (1998), which is hereby incorporatedby reference in its entirety), characterized by a 25 Hz splitting of the²H₂O line. Both experiments were performed at once each on Varian INOVA600 and 750 spectrometers equipped, respectively, with cryogenic andconventional triple resonance probes. To ensure identical r.f. pulseduty cycle, central peak spectra (Kim et al., J. Am. Chem. Soc.125:1385-1393 (2003), which is hereby incorporated by reference in itsentirety) were acquired with the same pulse scheme by successivelyomitting coupling evolutions (FIG. 48). Spectra on the 750 MHz (600 MHz)spectrometer were acquired with 50 complex points and 32 (16) transientsper free induction decay (FID) resulting in a total acquisition time of˜24 (12) hours for the full set of GFT experiments (i.e., basic as wellas central peak spectra). No linear prediction was employed and the timedomain signal was extended in the GFT dimension to 4096 complex pointsby zero-filling prior to Fourier transformation (FT).

Example 29 J-GFT (6,2)D (H^(α)—C^(α)—CO)—N—HN: Measurement of One-BondRDCs

Data analysis of the experimentally observed peak pattern for theZ-domain sample yielded two sets (“600 MHz” and “750 MHz” data sets) of44 ¹⁵N—¹H^(N), ¹⁵N—¹³C′, ¹³C^(α)—¹³C′ and ¹³C^(α)—¹H^(α) accuratelymeasurable RDCs out of the 50 observable peaks (corresponding to a yieldof ˜88%). These RDCs were further analyzed for accuracy and precision asdescribed in the following. Accuracy of RDC measurement was confirmed bycomparison of the “750 MHz” data sets (corrected for the phase errorsresulting from J-mismatch) with values obtained from conventional 2DIPAP (Ottiger et al., J. Magn. Reson. 131:373-378 (1998), which ishereby incorporated by reference in its entirety) or ω₁-coupled 2Dspectra recorded at the same field strength. A root mean squaredeviation (rmsd) (and correlation coefficient) of 2.0 Hz (0.96) and 0.8Hz (0.85) was obtained, respectively, for ¹J_(NH) and ¹J_(NC′)couplings. Notably, since the couplings were extracted from the full setcomprising both basic and central peak GFT spectra encoding all the fourone-bond dipolar couplings, such accuracy was equally expected also for¹J_(C)α_(C′) and ¹J_(C)α_(H)α couplings.

In sum, J-GFT (6,2)D (H^(α)—C^(α)—CO)—N—HN promises to be a valuable newexperiment for measurement of mutually correlated ¹⁵N—¹H^(N), ¹⁵N—¹³C′,¹³C^(α)—¹³C and ¹³C^(α)—¹H^(α) couplings in proteins. Measurement ofcorrelated RDCs can be combined with chemical shift detectedmultidimensional NMR experiments for aid in resonance assignments (Tianet al., J. Am. Chem. Soc. 123:11791-11796 (2001); Zweckstetter et al.,J. Am. Chem. Soc. 123:9490-9491 (2001), which are hereby incorporated byreference in their entirety). For protein with known 3D structure,(6,2)D (H^(α)—C^(α)—CO)—N—HN can be used for measurement of mutuallycorrelated RDCs for backbone assignments without the need for sequentialconnectivity information (Jung et al., J. Biomol. NMR 30:25-35 (2004),which is hereby incorporated by reference in its entirety). While thepresent scheme of the J-GFT experiment is based on an “out-and-stay”type of experiment (Cavanagh et al., Protein NMR Spectroscopy AcademicPress: San Diego, Calif. (1996), which is hereby incorporated byreference in its entirety), analogues “out-and-back” HN-detected J-GFTexperiments can be easily devised for application to larger and/ordeuterated proteins. Further, since only evolution due to one-bondscalar/dipolar coupling takes place during the ¹H^(α)—¹³C^(α),¹³C^(α)—¹³C′ and ¹³C′—¹⁵N INEPT transfers, the existing delays in thistime period can be additionally used for chemical shift evolution of therespective spins to gain dispersion, either in a separate indirectdimension or/and jointly with ¹⁵N chemical shift and one-bond couplingsin the GFT dimension. This provides new avenues to study proteins withhigh chemical shift degeneracy.

Although the invention has been described in detail, for the purpose ofillustration, it is understood that such detail is for that purpose andvariations can be made therein by those skilled in the art withoutdeparting from the spirit and scope of the invention which is defined bythe following claims.

1. A method of conducting a (5,3) dimensional (D)[HN{N,CO}{C ^(αβ) C^(α)}] G-matrix Fourier transformation (GFT) nuclear magnetic resonance(NMR) experiment, said method comprising: providing a sample, whereinsaid sample is a protein molecule having two consecutive amino acidresidues, i−1 and i, and the chemical shift values for the followingnuclei are measured: (1) α- and β-carbons of amino acid residues i andi−1, ¹³C^(α/β) _(i/i-1); (2) a polypeptide backbone amide nitrogen ofamino acid residue i, ¹⁵N_(i); (3) a polypeptide backbone carbonylcarbon of amino acid residue i−1, ¹³C′_(i-1); and (4) a polypeptidebackbone amide proton of amino acid residue i, ¹H^(N) _(i); applyingradiofrequency pulses for a 5D FT NMR experiment to the sample;selecting a first set of 2 indirect chemical shift evolution periods ofthe 5D FT NMR experiment, ¹³C^(α/β) _(i/i-1) and ¹³C^(α) _(i/i-1);jointly sampling the first set of 2 indirect chemical shift evolutionperiods in a first indirect time domain dimension, t₁(¹³C^(α/β)_(i/i-1), ¹³C^(α) _(i/i-1)); selecting a second set of 2 indirectchemical shift evolution periods of the 5D FT NMR experiment, ¹⁵N_(i)and ¹³C′_(i-1); jointly sampling the second set of 2 indirect chemicalshift evolution periods in a second indirect time domain dimension,t₂(¹⁵N_(i), ¹³C′_(i-1)); independently cosine and sine modulating NMRsignals detected in a direct dimension to generate 3D basic NMR spectracomprising frequency domain signals having a chemical shift multipletwith 4 components resulting from each of 2 chemical shift doubletcomponents in a first frequency domain dimension, ω₁(¹³C^(α/β),¹³C^(α)), giving rise to 2 chemical shift doublet components in a secondfrequency domain dimension, ω₂(¹⁵N, ¹³C′), thereby enablingphase-sensitive sampling of all jointly sampled 4 indirect chemicalshift evolution periods; and transforming the 3D basic NMR spectra into3D phase-sensitively edited basic NMR spectra, wherein the 4 chemicalshift multiplet components of the 3D basic NMR spectra are edited toyield 3D phase-sensitively edited basic NMR spectra having individualchemical shift multiplet components.
 2. The method according to claim 1,wherein said transforming is carried out by applying a G-matrix definedas ${{\hat{G}(1)} = {\begin{bmatrix}1 & i \\1 & {- i}\end{bmatrix} \otimes \left\lbrack {1i} \right\rbrack}},$ whereini=√{square root over (−1)}, along the first and second indirect timedomain dimensions under conditions effective to edit the chemical shiftmultiplet components in the time domain.
 3. The method according toclaim 1, wherein said transforming is carried out by applying a F-matrixdefined as ${\hat{F}(1)} = \begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}$ along the first and second frequency domain dimensionsunder conditions effective to edit the chemical shift multipletcomponents in the frequency domain.
 4. The method according to claim 1,wherein said applying radiofrequency pulses comprises applyingradiofrequency pulses for a 5D FT NMR experiment according to the schemeshown in FIG.
 5. 5. A method of conducting a (5,3) dimensional (D)[HN{NCO}{C ^(αβ) C ^(α)}] G-matrix Fourier transformation (GFT) nuclearmagnetic resonance (NMR) experiment, said method comprising: providing asample, wherein said sample is a protein molecule having two consecutiveamino acid residues, i−1 and i, and the chemical shift values for thefollowing nuclei are measured: (1) α- and β-carbons of amino acidresidue i−1, ¹³C^(α/β) _(i-1); (2) a polypeptide backbone amide nitrogenof amino acid residue i, ¹⁵N_(i); (3) a polypeptide backbone carbonylcarbon of amino acid residue i−1, ¹³C′_(i-1); and (4) a polypeptidebackbone amide proton of amino acid residue i, ¹H^(N) _(i); applyingradiofrequency pulses for a 5D FT NMR experiment to the sample;selecting a first set of 2 indirect chemical shift evolution periods ofthe 5D FT NMR experiment, ¹³C^(α/β) _(i-1) and ¹³C^(α) _(i-1); jointlysampling the first set of 2 indirect chemical shift evolution periods ina first indirect time domain dimension, t₁(¹³C^(α/β) _(i-1), ¹³C^(α)_(i-1)); selecting a second set of 2 indirect chemical shift evolutionperiods of the 5D FT NMR experiment, ¹⁵N_(i) and ¹³C′_(i-1); jointlysampling the second set of 2 indirect chemical shift evolution periodsin a second indirect time domain dimension, t₂(¹⁵N_(i), ¹³C′_(i-1));independently cosine and sine modulating NMR signals detected in adirect dimension to generate 3D basic NMR spectra comprising frequencydomain signals having a chemical shift multiplet with 4 componentsresulting from each of 2 chemical shift doublet components in a firstfrequency domain dimension, ω₁(¹³C^(α/β), ¹³C^(α)), giving rise to 2chemical shift doublet components in a second frequency domaindimension, ω₂(¹⁵N, ¹³C′), thereby enabling phase-sensitive sampling ofall jointly sampled 4 indirect chemical shift evolution periods; andtransforming the 3D basic NMR spectra into 3D phase-sensitively editedbasic NMR spectra, wherein the 4 chemical shift multiplet components ofthe 3D basic NMR spectra are edited to yield 3D phase-sensitively editedbasic NMR spectra having individual chemical shift multiplet components.6. The method according to claim 5, wherein said transforming is carriedout by applying a G-matrix defined as ${{\hat{G}(1)} = {\begin{bmatrix}1 & {\mathbb{i}} \\1 & {- {\mathbb{i}}}\end{bmatrix} \otimes \left\lbrack {1{\mathbb{i}}} \right\rbrack}},$wherein i=√{square root over (−1)}, along the first and second indirecttime domain dimensions under conditions effective to edit the chemicalshift multiplet components in the time domain.
 7. The method accordingto claim 5, wherein said transforming is carried out by applying aF-matrix defined as ${\hat{F}(1)} = \begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}$ along the first and second frequency domain dimensionsunder conditions effective to edit the chemical shift multipletcomponents in the frequency domain.
 8. The method according to claim 5,wherein said applying radiofrequency pulses comprises applyingradiofrequency pulses for a 5D FT NMR experiment according to the schemeshown in FIG.
 6. 9. A method of conducting a (5,3) dimensional (D)[HN{NC ^(α)}{C ^(αβ) C ^(α)}] G-matrix Fourier transformation (GFT)nuclear magnetic resonance (NMR) experiment, said method comprising:providing a sample, wherein said sample is a protein molecule having twoconsecutive amino acid residues, i−1 and i, and the chemical shiftvalues for the following nuclei are measured: (1) α- and β-carbons ofamino acid residue i and i−1, ¹³C^(α/β) _(i/i-1); (2) a polypeptidebackbone amide nitrogen of amino acid residue i, ¹⁵N_(i); and (3) apolypeptide backbone amide proton of amino acid residue i, ¹H^(N) _(i);applying radiofrequency pulses for a 5D FT NMR experiment to the sample;selecting a first set of 2 indirect chemical shift evolution periods ofthe 5D FT NMR experiment, ¹³C^(α/β) _(i/i-1) and ¹³C^(α) _(i/i-1);jointly sampling the first set of 2 indirect chemical shift evolutionperiods in a first indirect time domain dimension, t₁(¹³C^(α/β)_(i/i-1), ¹³C^(α) _(i/i-1)); selecting a second set of 2 indirectchemical shift evolution periods of the 5D FT NMR experiment, ¹⁵N_(i)and ¹³C^(α) _(i/i-1); jointly sampling the second set of 2 indirectchemical shift evolution periods in a second indirect time domaindimension, t₂(¹⁵N_(i), ¹³C^(α) _(i/i-1)); independently cosine and sinemodulating NMR signals detected in a direct dimension to generate 3Dbasic NMR spectra comprising frequency domain signals having a chemicalshift multiplet with 4 components resulting from each of 2 chemicalshift doublet components in a first frequency domain dimension,ω₁(¹³C^(α/β), ¹³C^(α)), giving rise to 2 chemical shift doubletcomponents in a second frequency domain dimension, ω₂(¹⁵N, ¹³C^(α)),thereby enabling phase-sensitive sampling of all jointly sampled 4indirect chemical shift evolution periods; and transforming the 3D basicNMR spectra into 3D phase-sensitively edited basic NMR spectra, whereinthe 4 chemical shift multiplet components of the 3D basic NMR spectraare edited to yield 3D phase-sensitively edited basic NMR spectra havingindividual chemical shift multiplet components.
 10. The method accordingto claim 9, wherein said transforming is carried out by applying aG-matrix defined as ${{\hat{G}(1)} = {\begin{bmatrix}1 & {\mathbb{i}} \\1 & {- {\mathbb{i}}}\end{bmatrix} \otimes \left\lbrack {1{\mathbb{i}}} \right\rbrack}},$wherein i=√{square root over (−1)}, along the first and second indirecttime domain dimensions under conditions effective to edit the chemicalshift multiplet components in the time domain.
 11. The method accordingto claim 9, wherein said transforming is carried out by applying aF-matrix defined as ${\hat{F}(1)} = \begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}$ along the first and second frequency domain dimensionsunder conditions effective to edit the chemical shift multipletcomponents in the frequency domain.
 12. The method according to claim 9,wherein said applying radiofrequency pulses comprises applyingradiofrequency pulses for a 5D FT NMR experiment according to the schemeshown in FIG.
 13. 13. A method of conducting a (5,3) dimensional (D)[HN{N(CO)C ^(α)}{C ^(αβ) C ^(α)}] G-matrix Fourier transformation (GFT)nuclear magnetic resonance (NMR) experiment, said method comprising:providing a sample, wherein said sample is a protein molecule having twoconsecutive amino acid residues, i−1 and i, and the chemical shiftvalues for the following nuclei are measured: (1) α- and β-carbons ofamino acid residue i−1, ¹³C^(α/β) _(i-1); (2) a polypeptide backboneamide nitrogen of amino acid residue i, ¹⁵N_(i); and (3) a polypeptidebackbone amide proton of amino acid residue i, ¹H^(N) _(i); applyingradiofrequency pulses for a 5D FT NMR experiment to the sample;selecting a first set of 2 indirect chemical shift evolution periods ofthe 5D FT NMR experiment, ¹³C^(α/β) _(i-1) and ¹³C^(α) _(i-1); jointlysampling the first set of 2 indirect chemical shift evolution periods ina first indirect time domain dimension, t₁(¹³C^(αβ) _(i-1), ¹³C^(α)_(i-1)); selecting a second set of 2 indirect chemical shift evolutionperiods of the 5D FT NMR experiment, ¹⁵N_(i) and ¹³C^(α) _(i-1); jointlysampling the second set of 2 indirect chemical shift evolution periodsin a second indirect time domain dimension, t₂(¹⁵N_(i), ¹³C^(α) _(i-1));independently cosine and sine modulating NMR signals detected in adirect dimension to generate 3D basic NMR spectra comprising frequencydomain signals having a chemical shift multiplet with 4 componentsresulting from each of 2 chemical shift doublet components in a firstfrequency domain dimension, ω₁(¹³C^(α/β), ¹³C^(α)), giving rise to 2chemical shift doublet components in a second frequency domaindimension, ω₂(¹⁵N, ¹³C^(α)), thereby enabling phase-sensitive samplingof all jointly sampled 4 indirect chemical shift evolution periods; andtransforming the 3D basic NMR spectra into 3D phase-sensitively editedbasic NMR spectra, wherein the 4 chemical shift multiplet components ofthe 3D basic NMR spectra are edited to yield 3D phase-sensitively editedbasic NMR spectra having individual chemical shift multiplet components.14. The method according to claim 13, wherein said transforming iscarried out by applying a G-matrix defined as${{\hat{G}(1)} = {\begin{bmatrix}1 & {\mathbb{i}} \\1 & {- {\mathbb{i}}}\end{bmatrix} \otimes \left\lbrack {1{\mathbb{i}}} \right\rbrack}},$wherein i=√{square root over (−1)}, along the first and second indirecttime domain dimensions under conditions effective to edit the chemicalshift multiplet components in the time domain.
 15. The method accordingto claim 13, wherein said transforming is carried out by applying aF-matrix defined as ${\hat{F}(1)} = \begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}$ along the first and second frequency domain dimensionsunder conditions effective to edit the chemical shift multipletcomponents in the frequency domain.
 16. The method according to claim13, wherein said applying radiofrequency pulses comprises applyingradiofrequency pulses for a 5D FT NMR experiment according to the schemeshown in FIG.
 14. 17. A method of conducting a (5,3) dimensional (D)[HN{N,CO}{C ^(α) H ^(α)}] G-matrix Fourier transformation (GFT) nuclearmagnetic resonance (NMR) experiment, said method comprising: providing asample, wherein said sample is a protein molecule having two consecutiveamino acid residues, i−1 and i, and the chemical shift values for thefollowing nuclei are measured: (1) α-carbon of amino acid residues i andi−1, ¹³C^(α) _(i/i-1); (2) α-proton of amino acid residues i and i−1,¹H^(α) _(i/i-1); (3) a polypeptide backbone amide nitrogen of amino acidresidue i, ¹⁵N_(i); (4) a polypeptide backbone carbonyl carbon of aminoacid residue i−1, ¹³C′_(i-1); and (5) a polypeptide backbone amideproton of amino acid residue i, ¹H^(N) _(i); applying radiofrequencypulses for a 5D FT NMR experiment to the sample; selecting a first setof 2 indirect chemical shift evolution periods of the 5D FT NMRexperiment, ¹H^(α) _(i/i-1) and ¹³C^(α) _(i/i-1); jointly sampling thefirst set of 2 indirect chemical shift evolution periods in a firstindirect time domain dimension, t₁(¹H^(α) _(i/i-1), ¹³C^(α) _(i/i-1));selecting a second set of 2 indirect chemical shift evolution periods ofthe 5D FT NMR experiment, ¹⁵N_(i) and ¹³C′_(i-1); jointly sampling thesecond set of 2 indirect chemical shift evolution periods in a secondindirect time domain dimension, t₂(¹⁵N_(i), ¹³C′_(i-1)); independentlycosine and sine modulating NMR signals detected in a direct dimension togenerate 3D basic NMR spectra comprising frequency domain signals havinga chemical shift multiplet with 4 components resulting from each of 2chemical shift doublet components in a first frequency domain dimension,ω₁(¹H^(α), ¹³C^(α)), giving rise to 2 chemical shift doublet componentsin a second frequency domain dimension, ω₂(¹⁵N, ¹³C′), thereby enablingphase-sensitive sampling of all jointly sampled 4 indirect chemicalshift evolution periods; and transforming the 3D basic NMR spectra into3D phase-sensitively edited basic NMR spectra, wherein the 4 chemicalshift multiplet components of the 3D basic NMR spectra are edited toyield 3D phase-sensitively edited basic NMR spectra having individualchemical shift multiplet components.
 18. The method according to claim17, wherein said transforming is carried out by applying a G-matrixdefined as ${{\hat{G}(1)} = {\begin{bmatrix}1 & {\mathbb{i}} \\1 & {- {\mathbb{i}}}\end{bmatrix} \otimes \left\lbrack {1{\mathbb{i}}} \right\rbrack}},$wherein i=√{square root over (−1)}, along the first and second indirecttime domain dimensions under conditions effective to edit the chemicalshift multiplet components in the time domain.
 19. The method accordingto claim 17, wherein said transforming is carried out by applying aF-matrix defined as ${\hat{F}(1)} = \begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}$ along the first and second frequency domain dimensionsunder conditions effective to edit the chemical shift multipletcomponents in the frequency domain.
 20. The method according to claim17, wherein said applying radiofrequency pulses comprises applyingradiofrequency pulses for a 5D FT NMR experiment according to the schemeshown in FIG.
 18. 21. A method of conducting a (5,3) dimensional (D) [{H^(α) C ^(α)}{CON}HN] G-matrix Fourier transformation (GFT) nuclearmagnetic resonance (NMR) experiment, said method comprising: providing asample, wherein said sample is a protein molecule having two consecutiveamino acid residues, i−1 and i, and the chemical shift values for thefollowing nuclei are measured: (1) α-carbon of amino acid residue i−1,¹³C^(α) _(i-1); (2) α-proton of amino acid residue i−1, ¹H^(α) _(i-1);(3) a polypeptide backbone amide nitrogen of amino acid residue i,¹⁵N_(i); (4) a polypeptide backbone carbonyl carbon of amino acidresidue i−1, ¹³C′_(i-1); and (5) a polypeptide backbone amide proton ofamino acid residue i, ¹H^(N) _(i); applying radiofrequency pulses for a5D FT NMR experiment to the sample; selecting a first set of 2 indirectchemical shift evolution periods of the 5D FT NMR experiment, ¹H^(α)_(i-1) and ¹³C^(α) _(i-1); jointly sampling the first set of 2 indirectchemical shift evolution periods in a first indirect time domaindimension, t₁(¹H^(α) _(i-1), ¹³C^(α) _(i-1)); selecting a second set of2 indirect chemical shift evolution periods of the 5D FT NMR experiment,¹⁵N_(i) and ¹³C′_(i-1); jointly sampling the second set of 2 indirectchemical shift evolution periods in a second indirect time domaindimension, t₂(¹⁵N_(i), ¹³C′_(i-1)); independently cosine and sinemodulating NMR signals detected in a direct dimension to generate 3Dbasic NMR spectra comprising frequency domain signals having a chemicalshift multiplet with 4 components resulting from each of 2 chemicalshift doublet components in a first frequency domain dimension,ω₁(¹H^(α), ¹³C^(α)), giving rise to 2 chemical shift doublet componentsin a second frequency domain dimension, ω₂(¹⁵N, ¹³C′), thereby enablingphase-sensitive sampling of all jointly sampled 4 indirect chemicalshift evolution periods; and transforming the 3D basic NMR spectra into3D phase-sensitively edited basic NMR spectra, wherein the 4 chemicalshift multiplet components of the 3D basic NMR spectra are edited toyield 3D phase-sensitively edited basic NMR spectra having individualchemical shift multiplet components.
 22. The method according to claim21, wherein said transforming is carried out by applying a G-matrixdefined as ${{\hat{G}(1)} = {\begin{bmatrix}1 & {\mathbb{i}} \\1 & {- {\mathbb{i}}}\end{bmatrix} \otimes \left\lbrack {1{\mathbb{i}}} \right\rbrack}},$wherein i=√{square root over (−1)}, along the first and second indirecttime domain dimensions under conditions effective to edit the chemicalshift multiplet components in the time domain.
 23. The method accordingto claim 21, wherein said transforming is carried out by applying aF-matrix defined as ${\hat{F}(1)} = \begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}$ along the first and second frequency domain dimensionsunder conditions effective to edit the chemical shift multipletcomponents in the frequency domain.
 24. The method according to claim21, wherein said applying radiofrequency pulses comprises applyingradiofrequency pulses for a 5D FT NMR experiment according to the schemeshown in FIG.
 19. 25. A method of conducting a (6,3) dimensional (D) [{H^(αβ) C ^(αβ) C ^(α)}{CON}HN] G-matrix Fourier transformation (GFT)nuclear magnetic resonance (NMR) experiment, said method comprising:providing a sample, wherein said sample is a protein molecule having twoconsecutive amino acid residues, i−1 and i, and the chemical shiftvalues for the following nuclei are measured: (1) α- and β-carbons ofamino acid residue i−1, ¹³C^(α/β) _(i-1); (2) α- and β-protons of aminoacid residue i−1, ¹H^(α/β) _(i-1); (3) a polypeptide backbone carbonylcarbon of amino acid residue i−1, ¹³C′_(i-1); (4) a polypeptide backboneamide nitrogen of amino acid residue i, ¹⁵N_(i); and (5) a polypeptidebackbone amide proton of amino acid residue i, ¹H^(N) _(i); applyingradiofrequency pulses for a 6D FT NMR experiment to the sample;selecting a first group of 3 indirect chemical shift evolution periodsof the 6D FT NMR experiment, ¹H^(α/β) _(i-1), ¹³C^(α/β) _(i-1), and¹³C^(α) _(i-1); jointly sampling the first group of 3 indirect chemicalshift evolution periods in a first indirect time domain dimension,t₁(¹H^(α/β) _(i-1), ¹³C^(α/β) _(i-1), ¹³C^(α) _(i-1)); selecting asecond group of 2 indirect chemical shift evolution periods of the 6D FTNMR experiment, ¹⁵N_(i) and ¹³C′_(i-1); jointly sampling the secondgroup of 2 indirect chemical shift evolution periods in a secondindirect time domain dimension, t₂(¹⁵N_(i), ¹³C′_(i-1)); independentlycosine and sine modulating NMR signals detected in a direct dimension togenerate 3D basic NMR spectra comprising frequency domain signals havinga chemical shift multiplet with 8 components resulting from each of 4chemical shift doublet components in a first frequency domain dimension,ω₁(¹³C^(α/β), ¹³C^(α)), giving rise to 2 chemical shift doubletcomponents in a second frequency domain dimension, ω₂(¹⁵N, ¹³C′),thereby enabling phase-sensitive sampling of all jointly sampled 5indirect chemical shift evolution periods; and transforming the 3D basicNMR spectra into 3D phase-sensitively edited basic NMR spectra, whereinthe 8 chemical shift multiplet components of the 3D basic NMR spectraare edited to yield 3D phase-sensitively edited basic NMR spectra havingindividual chemical shift multiplet components.
 26. The method accordingto claim 25, wherein said transforming is carried out by applying aG-matrix defined as ${{\hat{G}(2)} = {\begin{bmatrix}1 & i \\1 & {- i}\end{bmatrix} \otimes \begin{bmatrix}1 & i \\1 & {- i}\end{bmatrix} \otimes \left\lbrack {1i} \right\rbrack}},$ whereini=√{square root over (−1)}, along the first indirect time domaindimension and applying a G-matrix defined as${\hat{G}(1)} = {\begin{bmatrix}1 & i \\1 & {- i}\end{bmatrix} \otimes \left\lbrack {1i} \right\rbrack}$ along the secondindirect time domain dimension under conditions effective to edit thechemical shift multiplet components in the time domain.
 27. The methodaccording to claim 25, wherein said transforming is carried out byapplying a F-matrix defined as {circumflex over (F)}(2)={circumflex over(F)}(1){circle around (×)}{circumflex over (F)}(1), wherein${{\hat{F}(1)} = \begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}},$ along the first frequency domain dimension and applyinga F-matrix defined as ${\hat{F}(1)} = \begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}$ along the second frequency domain dimension underconditions effective to edit the chemical shift multiplet components inthe frequency domain.
 28. The method according to claim 25, wherein saidapplying radiofrequency pulses comprises applying radiofrequency pulsesfor a 6D FT NMR experiment according to the scheme shown in FIG.
 24. 29.A method of conducting a (5,3) dimensional (D) [HC(C)C—CH] G-matrixFourier transformation (GFT) nuclear magnetic resonance (NMR)experiment, said method comprising: providing a sample, wherein saidsample is a protein molecule and the chemical shift values for thefollowing nuclei are measured: (1) a proton, ¹H; (2) a carbon coupled to¹H, ¹³C; (3) a carbon coupled, via another carbon, to ¹³C,¹³C^(coupled); and (4) a proton coupled to ¹³C^(coupled), ¹H^(coupled),wherein the chemical shift of ¹³C^(coupled) provides signal dispersionin an indirect dimension; applying radiofrequency pulses for a 5D FT NMRexperiment to the sample; selecting 3 indirect chemical shift evolutionperiods of the 5D FT NMR experiment, ¹H, ¹³C, and ¹³C^(coupled); jointlysampling the 3 indirect chemical shift evolution periods in an indirecttime domain dimension, t₁(¹H, ¹³C, ¹³C^(coupled)); independently cosineand sine modulating NMR signals detected in a direct dimension togenerate 3D basic NMR spectra comprising frequency domain signals with 4chemical shift multiplet components, thereby enabling phase-sensitivesampling of all jointly sampled 3 indirect chemical shift evolutionperiods; and transforming the 3D basic NMR spectra into 3Dphase-sensitively edited basic NMR spectra, wherein the 4 chemical shiftmultiplet components of the 3D basic NMR spectra are edited to yield 3Dphase-sensitively edited basic NMR spectra having individual chemicalshift multiplet components.
 30. The method according to claim 29,wherein said transforming is carried out by applying a G-matrix definedas ${{\hat{G}(2)} = {\begin{bmatrix}1 & i \\1 & {- i}\end{bmatrix} \otimes \begin{bmatrix}1 & i \\1 & {- i}\end{bmatrix} \otimes \left\lbrack {1i} \right\rbrack}},$ whereini=√{square root over (−1)}, under conditions effective to edit thechemical shift multiplet components in a time domain.
 31. The methodaccording to claim 29, wherein said transforming is carried out byapplying a F-matrix defined as {circumflex over (F)}(2)={circumflex over(F)}(1){circle around (×)}{circumflex over (F)}(1), wherein${{\hat{F}(1)} = \begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}},$ under conditions effective to edit the chemical shiftmultiplet components in a frequency domain.
 32. The method according toclaim 29 further comprising: repeating once said jointly sampling, saidindependently cosine and sine modulating, and said transforming, whereinsaid jointly sampling comprises jointly sampling 2 indirect chemicalshift evolution periods out of the 3 indirect chemical shift evolutionperiods, under conditions effective to generate a first order centralpeak NMR spectrum.
 33. The method according to claim 29, wherein saidapplying radiofrequency pulses comprises applying radiofrequency pulsesfor a 5D FT NMR experiment according to the scheme shown in FIG.
 27. 34.A method of conducting a longitudinal aromatic proton relaxationoptimized (4,3) dimensional (D) [HCCH] G-matrix Fourier transformation(GFT) nuclear magnetic resonance (NMR) experiment, said methodcomprising: providing a sample, wherein said sample is a proteinmolecule and the chemical shift values for the following nuclei aremeasured: (1) an aromatic proton, ¹H; (2) an aromatic carbon coupled to¹H, ¹³C; (3) a carbon coupled to ¹³C, ¹³C^(coupled); and (4) a protoncoupled to ¹³C^(coupled), ¹H^(coupled); applying radiofrequency pulsesfor a 4D FT NMR experiment to the sample under conditions effective toallow longitudinal relaxation optimization of the aromatic protons;selecting 2 indirect chemical shift evolution periods of the 4D FT NMRexperiment, ¹H and ¹³C; jointly sampling the 2 indirect chemical shiftevolution periods in an indirect time domain dimension, t₁(¹H, ¹³C);independently cosine and sine modulating NMR signals detected in adirect dimension to generate 3D basic NMR spectra comprising frequencydomain signals with 2 chemical shift doublet components, therebyenabling phase-sensitive sampling of the jointly sampled 2 indirectchemical shift evolution periods; and transforming the 3D basic NMRspectra into 3D phase-sensitively edited basic NMR spectra, wherein the2 chemical shift doublet components of the 3D basic NMR spectra areedited to yield 3D phase-sensitively edited basic NMR spectra havingindividual chemical shift doublet components.
 35. The method accordingto claim 34, wherein said transforming is carried out by applying aG-matrix defined as ${{\hat{G}(1)} = {\begin{bmatrix}1 & i \\1 & {- i}\end{bmatrix} \otimes \left\lbrack {1i} \right\rbrack}},$ whereini=√{square root over (−1)}, under conditions effective to edit thechemical shift doublet components in a time domain.
 36. The methodaccording to claim 34, wherein said transforming is carried out byapplying a F-matrix defined as ${{\hat{F}(1)} = \begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}},$ under conditions effective to edit the chemical shiftdoublet components in a frequency domain.
 37. The method according toclaim 34, wherein said applying radiofrequency pulses comprises applyingradiofrequency pulses for a 4D FT NMR experiment according to the schemeshown in FIG.
 32. 38. A method of conducting a longitudinal aromaticproton relaxation optimized (4,3) dimensional (D) [HCCH] G-matrixFourier transformation (GFT) nuclear magnetic resonance (NMR)experiment, said method comprising: providing a sample, wherein saidsample is a protein molecule and the chemical shift values for thefollowing nuclei are measured: (1) an aromatic proton, ¹H; (2) anaromatic carbon coupled to ¹H, ¹³C; (3) a carbon coupled to ¹³C,¹³C^(coupled); and (4) a proton coupled to ¹³C^(coupled), ¹H^(coupled);applying radiofrequency pulses for a 4D FT NMR experiment to the sampleunder conditions effective to allow longitudinal relaxation optimizationof the aromatic protons; selecting 2 indirect chemical shift evolutionperiods of the 4D FT NMR experiment, ¹³C and ¹³C^(coupled); jointlysampling the 2 indirect chemical shift evolution periods in an indirecttime domain dimension, t₁(¹³C, ¹³C^(coupled)); independently cosine andsine modulating NMR signals detected in a direct dimension to generate3D basic NMR spectra comprising frequency domain signals with 2 chemicalshift doublet components, thereby enabling phase-sensitive sampling ofthe jointly sampled 2 indirect chemical shift evolution periods; andtransforming the 3D basic NMR spectra into 3D phase-sensitively editedbasic NMR spectra, wherein the 2 chemical shift doublet components ofthe 3D basic NMR spectra are edited to yield 3D phase-sensitively editedbasic NMR spectra having individual chemical shift doublet components.39. The method according to claim 38, wherein said transforming iscarried out by applying a G-matrix defined as${{\hat{G}(1)} = {\begin{bmatrix}1 & i \\1 & {- i}\end{bmatrix} \otimes \left\lbrack {1i} \right\rbrack}},$ whereini=√{square root over (−1)}, under conditions effective to edit thechemical shift doublet components in a time domain.
 40. The methodaccording to claim 38, wherein said transforming is carried out byapplying a F-matrix defined as ${{\hat{F}(1)} = \begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}},$ under conditions effective to edit the chemical shiftdoublet components in a frequency domain.
 41. A method of conducting alongitudinal aromatic proton relaxation optimized (4,3) dimensional (D)[HCCH] G-matrix Fourier transformation (GFT) nuclear magnetic resonance(NMR) experiment, said method comprising: providing a sample, whereinsaid sample is a protein molecule and the chemical shift values for thefollowing nuclei are measured: (1) an aromatic proton, ¹H; (2) anaromatic carbon coupled to ¹H, ¹³C; (3) a carbon coupled to ¹³C,¹³C^(coupled); and (4) a proton coupled to ¹³C^(coupled), ¹H^(coupled);applying radiofrequency pulses for a 4D FT NMR experiment to the sampleunder conditions effective to allow longitudinal relaxation optimizationof the aromatic protons; selecting 2 indirect chemical shift evolutionperiods of the 4D FT NMR experiment, ¹H and ¹³C^(coupled); jointlysampling the 2 indirect chemical shift evolution periods in an indirecttime domain dimension, t₁(¹H, ¹³C^(coupled)); independently cosine andsine modulating NMR signals detected in a direct dimension to generate3D basic NMR spectra comprising frequency domain signals with 2 chemicalshift doublet components, thereby enabling phase-sensitive sampling ofthe jointly sampled 2 indirect chemical shift evolution periods; andtransforming the 3D basic NMR spectra into 3D phase-sensitively editedbasic NMR spectra, wherein the 2 chemical shift doublet components ofthe 3D basic NMR spectra are edited to yield 3D phase-sensitively editedbasic NMR spectra having individual chemical shift doublet components.42. The method according to claim 41, wherein said transforming iscarried out by applying a G-matrix defined as${{\hat{G}(1)} = {\begin{bmatrix}1 & {\mathbb{i}} \\1 & {- {\mathbb{i}}}\end{bmatrix} \otimes \left\lbrack {1{\mathbb{i}}} \right\rbrack}},$wherein i=√{square root over (−1)}, under conditions effective to editthe chemical shift doublet components in a time domain.
 43. The methodaccording to claim 41, wherein said transforming is carried out byapplying a F-matrix defined as ${{\hat{F}(1)} = \begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}},$ under conditions effective to edit the chemical shiftdoublet components in a frequency domain.
 44. A method of conducting a(3,2) dimensional (D) <[¹ H ^(X) X]-nuclear Overhauser enhancementspectroscopy (NOESY)-[¹H]> G-matrix Fourier transformation (GFT) nuclearmagnetic resonance (NMR) experiment, said method comprising: providing asample, wherein said sample is a protein molecule and the chemical shiftvalues for the following nuclei are measured: (1) a proton, ¹H; (2) X,wherein X is an aliphatic carbon, ¹³C^(ali), an aromatic carbon,¹³C^(aro), or a nitrogen, ¹⁵N; and (3) a proton bound to X, ¹H^(X);applying radiofrequency pulses for a first 3D NOESY FT NMR experiment tothe sample; jointly sampling a first set of 2 indirect chemical shiftevolution periods of the 3D NOESY FT NMR experiment, ¹H^(X) and X, in anindirect time domain dimension, t₁(¹H^(X),X); independently cosine andsine modulating NMR signals detected in a direct dimension to generate2D basic NMR spectra comprising frequency domain signals with 2 chemicalshift doublet components, thereby enabling phase-sensitive sampling ofthe jointly sampled first set of 2 indirect chemical shift evolutionperiods; and transforming the 2D basic NMR spectra into 2Dphase-sensitively edited basic NMR spectra, wherein the 2 chemical shiftdoublet components of the 2D basic NMR spectra are edited to yield 2Dphase-sensitively edited basic NMR spectra having individual chemicalshift doublet components.
 45. The method according to claim 44, whereinchemical shift values for the following nuclei are further measured toconduct a (3,2)D <[¹ H ^(X) X/¹ H ^(Y) Y]-NOESY-[¹H]> GFT NMRexperiment: (1) Y, wherein Y is an aliphatic carbon, ¹³C^(ali), anaromatic carbon, ¹³C^(aro), or a nitrogen, ¹⁵N, and (2) ¹H^(Y), a protonbound to Y, wherein (a) said applying further comprises simultaneouslyapplying radiofrequency pulses for a second 3D NOESY FT NMR experimentto the sample, (b) said jointly sampling further comprisessimultaneously jointly sampling a second set of 2 indirect chemicalshift evolution periods of the 3D NOESY FT NMR experiment, ¹H^(Y) and Y,and (c) said independently cosine and sine modulating further comprisessimultaneous phase-sensitive sampling of the jointly sampled second setof 2 indirect chemical shift evolution periods.
 46. The method accordingto claim 45, wherein chemical shift values for the following nuclei arefurther measured to conduct a (3,2)D <[¹ H ^(X) X/¹ H ^(Y) Y/¹ H ^(Z)Z]-NOESY-[¹H]> GFT NMR experiment: (1) Z, wherein Z is an aliphaticcarbon, ¹³C^(ali), an aromatic carbon, ¹³C^(aro), or a nitrogen, ¹⁵N,and (2) ¹H^(Z), a proton bound to Z, wherein (a) said applying furthercomprises simultaneously applying radiofrequency pulses for a third 3DNOESY FT NMR experiment to the sample, (b) said jointly sampling furthercomprises simultaneously jointly sampling a third set of 2 indirectchemical shift evolution periods of the 3D NOESY FT NMR experiment,¹H^(Z) and Z, and (c) said independently cosine and sine modulatingfurther comprises simultaneous phase-sensitive sampling of the jointlysampled third set of 2 indirect chemical shift evolution periods. 47.The method according to claim 46, wherein said applying radiofrequencypulses comprises applying radiofrequency pulses for a simultaneous 3DNOESY FT NMR experiment according to the scheme shown in FIG.
 46. 48.The method according to claim 44, wherein said transforming is carriedout by applying a G-matrix defined as ${{\hat{G}(1)} = {\begin{bmatrix}1 & {\mathbb{i}} \\1 & {- {\mathbb{i}}}\end{bmatrix} \otimes \left\lbrack {1{\mathbb{i}}} \right\rbrack}},$wherein i=√{square root over (−1)}, under conditions effective to editthe chemical shift doublet components in a time domain.
 49. The methodaccording to claim 44, wherein said transforming is carried out byapplying a F-matrix defined as ${{\hat{F}(1)} = \begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}},$ under conditions effective to edit the chemical shiftdoublet components in a frequency domain.
 50. A method of conducting a(4,3) dimensional (D) <[¹ H ^(X) X]-nuclear Overhauser enhancementspectroscopy (NOESY)-[Y¹H^(Y)]> G-matrix Fourier transformation (GFT)nuclear magnetic resonance (NMR) experiment, said method comprising:providing a sample, wherein said sample is a protein molecule and thechemical shift values for the following nuclei are measured: (1) X,wherein X is an aliphatic carbon, ¹³C^(ali), an aromatic carbon,¹³C^(aro), or a nitrogen, ¹⁵N; (2) a proton bound to X, ¹H^(X); (3) Y,wherein Y is an aliphatic carbon, ¹³C^(ali), an aromatic carbon,¹³C^(aro), or a nitrogen, ¹⁵N; and (4) a proton bound to Y, ¹H^(Y);applying radiofrequency pulses for a first 4D NOESY FT NMR experiment tothe sample; selecting a first set of 2 indirect chemical shift evolutionperiods of the 4D NOESY FT NMR experiment, ¹H^(X) and X; jointlysampling the first set of 2 indirect chemical shift evolution periods inan indirect time domain dimension, t₁(¹H^(X),X); independently cosineand sine modulating NMR signals detected in a direct dimension togenerate 3D basic NMR spectra comprising frequency domain signals with 2chemical shift doublet components, thereby enabling phase-sensitivesampling of the jointly sampled 2 indirect chemical shift evolutionperiods; and transforming the 3D basic NMR spectra into 3Dphase-sensitively edited basic NMR spectra, wherein the 2 chemical shiftdoublet components of the 3D basic NMR spectra are edited to yield 3Dphase-sensitively edited basic NMR spectra having individual chemicalshift doublet components.
 51. The method according to claim 50, whereinchemical shift values for the following nuclei are further measured toconduct a (4,3)D <[¹ H ^(X) X/¹ H ^(X′) X′]-NOESY-[Y¹H^(Y)/Y′¹H^(Y′)]>GFT NMR experiment: (1) X′, wherein X′ is an aliphatic carbon,¹³C^(ali), an aromatic carbon, ¹³C^(aro), or a nitrogen, ¹⁵N; (2) aproton bound to X′, ¹H^(X′); (3) Y′, wherein Y′ is an aliphatic carbon,¹³C^(ali), an aromatic carbon, ¹³C^(aro), or a nitrogen, ¹⁵N; and (4) aproton bound to Y′, ¹H^(Y′), wherein (a) said applying further comprisessimultaneously applying radiofrequency pulses for a second 4D NOESY FTNMR experiment to the sample, (b) said jointly sampling furthercomprises simultaneously jointly sampling a second set of 2 indirectchemical shift evolution periods of the 4D NOESY FT NMR experiment,¹H^(Y) and Y, and (c) said independently cosine and sine modulatingfurther comprises simultaneous phase-sensitive sampling of the jointlysampled second set of 2 indirect chemical shift evolution periods. 52.The method according to claim 51, wherein said applying comprisesapplying radiofrequency pulses for a simultaneous 4D NOESY FT NMRexperiment according to the scheme shown in FIG. 36(a).
 53. The methodaccording to claim 50, wherein said transforming is carried out byapplying a G-matrix defined as ${{\hat{G}(1)} = {\begin{bmatrix}1 & {\mathbb{i}} \\1 & {- {\mathbb{i}}}\end{bmatrix} \otimes \left\lbrack {1{\mathbb{i}}} \right\rbrack}},$wherein i=√{square root over (−1)}, under conditions effective to editthe chemical shift doublet components in a time domain.
 54. The methodaccording to claim 50, wherein said transforming is carried out byapplying a F-matrix defined as ${{\hat{F}(1)} = \begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}},$ under conditions effective to edit the chemical shiftdoublet components in a frequency domain.
 55. A method of conducting a(4,2) dimensional (D) <[¹ H ^(X) X]-nuclear Overhauser enhancementspectroscopy (NOESY)-[Y ¹H^(Y)]> G-matrix Fourier transformation (GFT)nuclear magnetic resonance (NMR) experiment, said method comprising:providing a sample, wherein said sample is a protein molecule and thechemical shift values for the following nuclei are measured: (1) X,wherein X is an aliphatic carbon, ¹³C^(ali), an aromatic carbon,¹³C^(aro), or a nitrogen, ¹⁵N; (2) a proton bound to X, ¹H^(X); (3) Y,wherein Y is an aliphatic carbon, ¹³C^(ali), an aromatic carbon,¹³C^(aro), or a nitrogen, ¹⁵N; and (4) a proton bound to Y, ¹H^(Y);applying radiofrequency pulses for a first 4D NOESY FT NMR experiment tothe sample; selecting a first group of 3 indirect chemical shiftevolution periods of the 4D NOESY FT NMR experiment, ¹H^(X), X, and Y;jointly sampling the first group of 3 indirect chemical shift evolutionperiods in an indirect time domain dimension, t₁(¹H^(X),X,Y);independently cosine and sine modulating NMR signals detected in adirect dimension to generate 2D basic NMR spectra comprising frequencydomain signals with 4 chemical shift multiplet components, therebyenabling phase-sensitive sampling of all jointly sampled 3 indirectchemical shift evolution periods; and transforming the 2D basic NMRspectra into 2D phase-sensitively edited basic NMR spectra, wherein the4 chemical shift multiplet components of the 2D basic NMR spectra areedited to yield 2D phase-sensitively edited basic NMR spectra havingindividual chemical shift multiplet components.
 56. The method accordingto claim 55, wherein chemical shift values for the following nuclei arefurther measured to conduct a (4,2)D <[¹ H ^(X) X/¹ H ^(X′) X′]-NOESY-[Y¹H^(Y)/Y′ ¹H^(Y′)]> GFT NMR experiment: (1) X′, wherein X′ is analiphatic carbon, ¹³C^(ali), an aromatic carbon, ¹³C^(aro), or anitrogen, ¹⁵N; (2) a proton bound to X′, ¹H^(X′); (3) Y′, wherein Y′ isan aliphatic carbon, ¹³C^(ali), an aromatic carbon, ¹³C^(aro), or anitrogen, ¹⁵N; and (4) a proton bound to Y′, ¹H^(Y′), wherein (a) saidapplying further comprises simultaneously applying radiofrequency pulsesfor a second 4D NOESY FT NMR experiment to the sample, (b) said jointlysampling further comprises simultaneously jointly sampling a secondgroup of 3 indirect chemical shift evolution periods of the 4D NOESY FTNMR experiment, ¹H^(X′), X′, and Y′, and (c) said independently cosineand sine modulating further comprises simultaneous phase-sensitivesampling of the second group of the jointly sampled indirect chemicalshift evolution periods.
 57. The method according to claim 55, whereinsaid transforming is carried out by applying a G-matrix defined as${{\hat{G}(2)} = {\begin{bmatrix}1 & {\mathbb{i}} \\1 & {- {\mathbb{i}}}\end{bmatrix} \otimes \begin{bmatrix}1 & {\mathbb{i}} \\1 & {- {\mathbb{i}}}\end{bmatrix} \otimes \left\lbrack {1{\mathbb{i}}} \right\rbrack}},$wherein i=√{square root over (−1)}, under conditions effective to editthe chemical shift multiplet components in a time domain.
 58. The methodaccording to claim 55, wherein said transforming is carried out byapplying a F-matrix defined as {circumflex over (F)}(2)={circumflex over(F)}(1){circle around (×)}{circumflex over (F)}(1), wherein${{\hat{F}(1)} = \begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}},$ under conditions effective to edit the chemical shiftmultiplet components in a frequency domain.
 59. The method according toclaim 55 further comprising: repeating once said jointly sampling, saidindependently cosine and sine modulating, and said transforming, whereinsaid jointly sampling comprises jointly sampling 2 indirect chemicalshift evolution periods out of the 3 indirect chemical shift evolutionperiods, under conditions effective to generate a first order centralpeak NMR spectrum.
 60. The method according to claim 55, wherein saidapplying radiofrequency pulses comprises applying radiofrequency pulsesfor a simultaneous 4D NOESY FT NMR experiment according to the schemeshown in FIG.
 44. 61. A method of conducting a (6,2) dimensional (D)[(H^(α)—C^(α)—CO)—N—HN] G-matrix Fourier transformation (GFT) nuclearmagnetic resonance (NMR) experiment, said method comprising: providing asample, wherein said sample is a protein molecule having two consecutiveamino acid residues, i−1 and i, and the chemical shift values for thefollowing nuclei: (1) a polypeptide backbone amide nitrogen of aminoacid residue i, ¹⁵N_(i); and (2) a polypeptide backbone amide proton ofamino acid residue i, ¹H^(N) _(i), are measured in combination with fourspin-spin couplings between (1) an α-proton of amino acid residue i−1,¹H^(α) _(i-1), and an α-carbon of amino acid residue i−1, ¹³C^(α)_(i-1); (2) an α-carbon of amino acid residue i−1, ¹³C^(α) _(i-1), and apolypeptide backbone carbonyl carbon of amino acid residue i−1,¹³C′_(i-1); (3) a polypeptide backbone carbonyl carbon of amino acidresidue i−1, ¹³C′_(i-1), and a polypeptide backbone amide nitrogen ofamino acid residue i, ¹⁵N_(i); (4) a polypeptide backbone amide nitrogenof amino acid residue i, ¹⁵N_(i), and a polypeptide backbone amideproton of amino acid residue i, ¹H^(N) _(i); applying radiofrequencypulses for a 6D FT NMR experiment to the sample; selecting an indirectchemical shift evolution period of the 6D FT NMR experiment, ¹⁵N_(i);jointly sampling the indirect chemical shift evolution period with fourindirect spin-spin coupling evolution periods resulting from samplingthe four spin-spin couplings; independently cosine and sine modulatingNMR signals detected in a direct dimension resulting from time evolutionof the indirect chemical shift and the four spin-spin couplings togenerate 2D basic NMR spectra comprising frequency domain signals with16 multiplet components, thereby enabling phase-sensitive sampling ofthe indirect chemical shift evolution period and the indirect spin-spincoupling evolution periods; and transforming the 2D basic NMR spectrainto 2D phase-sensitively edited basic NMR spectra, wherein the 16multiplet components of the 2D basic NMR spectra are edited to yield 2Dphase-sensitively edited basic NMR spectra having individual multipletcomponents.
 62. The method according to claim 61, wherein saidtransforming is carried out by applying a G-matrix defined as${{\hat{G}(4)} = {\begin{bmatrix}1 & {\mathbb{i}} \\1 & {- i}\end{bmatrix} \otimes \begin{bmatrix}1 & {\mathbb{i}} \\1 & {- {\mathbb{i}}}\end{bmatrix} \otimes \begin{bmatrix}1 & {\mathbb{i}} \\1 & {- {\mathbb{i}}}\end{bmatrix} \otimes \begin{bmatrix}1 & {\mathbb{i}} \\1 & {- {\mathbb{i}}}\end{bmatrix} \otimes \left\lbrack {1{\mathbb{i}}} \right\rbrack}},$wherein i=√{square root over (−1)}, under conditions effective to editthe multiplet components in a time domain.
 63. The method according toclaim 61, wherein said transforming is carried out by applying aF-matrix defined as {circumflex over (F)}(4)={circumflex over(F)}(1){circle around (×)}{circumflex over (F)}(1){circle around(×)}{circumflex over (F)}(1){circle around (×)}{circumflex over (F)}(1),wherein ${{\hat{F}(1)} = \begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}},$ under conditions effective to edit the multipletcomponents in a frequency domain.
 64. The method according to claim 61,wherein said applying radiofrequency pulses comprises applyingradiofrequency pulses for a 6D FT NMR experiment according to the schemeshown in FIG. 47.